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/*************************************************************************
ALGLIB 3.16.0 (source code generated 2019-12-19)
Copyright (c) Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _optimization_pkg_h
#define _optimization_pkg_h
#include "ap.h"
#include "alglibinternal.h"
#include "linalg.h"
#include "alglibmisc.h"
#include "solvers.h"
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (DATATYPES)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_CQMODELS) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t k;
double alpha;
double tau;
double theta;
ae_matrix a;
ae_matrix q;
ae_vector b;
ae_vector r;
ae_vector xc;
ae_vector d;
ae_vector activeset;
ae_matrix tq2dense;
ae_matrix tk2;
ae_vector tq2diag;
ae_vector tq1;
ae_vector tk1;
double tq0;
double tk0;
ae_vector txc;
ae_vector tb;
ae_int_t nfree;
ae_int_t ecakind;
ae_matrix ecadense;
ae_matrix eq;
ae_matrix eccm;
ae_vector ecadiag;
ae_vector eb;
double ec;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpg;
ae_matrix tmp2;
ae_bool ismaintermchanged;
ae_bool issecondarytermchanged;
ae_bool islineartermchanged;
ae_bool isactivesetchanged;
} convexquadraticmodel;
#endif
#if defined(AE_COMPILE_OPTGUARDAPI) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_bool nonc0suspected;
ae_bool nonc0test0positive;
ae_int_t nonc0fidx;
double nonc0lipschitzc;
ae_bool nonc1suspected;
ae_bool nonc1test0positive;
ae_bool nonc1test1positive;
ae_int_t nonc1fidx;
double nonc1lipschitzc;
ae_bool badgradsuspected;
ae_int_t badgradfidx;
ae_int_t badgradvidx;
ae_vector badgradxbase;
ae_matrix badgraduser;
ae_matrix badgradnum;
} optguardreport;
typedef struct
{
ae_bool positive;
ae_int_t fidx;
ae_vector x0;
ae_vector d;
ae_int_t n;
ae_vector stp;
ae_vector f;
ae_int_t cnt;
ae_int_t stpidxa;
ae_int_t stpidxb;
} optguardnonc0report;
typedef struct
{
ae_bool positive;
ae_int_t fidx;
ae_vector x0;
ae_vector d;
ae_int_t n;
ae_vector stp;
ae_vector f;
ae_int_t cnt;
ae_int_t stpidxa;
ae_int_t stpidxb;
} optguardnonc1test0report;
typedef struct
{
ae_bool positive;
ae_int_t fidx;
ae_int_t vidx;
ae_vector x0;
ae_vector d;
ae_int_t n;
ae_vector stp;
ae_vector g;
ae_int_t cnt;
ae_int_t stpidxa;
ae_int_t stpidxb;
} optguardnonc1test1report;
#endif
#if defined(AE_COMPILE_OPTSERV) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_vector norms;
ae_vector alpha;
ae_vector rho;
ae_matrix yk;
ae_vector idx;
ae_vector bufa;
ae_vector bufb;
} precbuflbfgs;
typedef struct
{
ae_int_t n;
ae_int_t k;
ae_vector d;
ae_matrix v;
ae_vector bufc;
ae_matrix bufz;
ae_matrix bufw;
ae_vector tmp;
} precbuflowrank;
typedef struct
{
ae_int_t n;
ae_int_t k;
ae_bool checksmoothness;
ae_vector dcur;
ae_int_t enqueuedcnt;
ae_vector enqueuedstp;
ae_vector enqueuedx;
ae_vector enqueuedfunc;
ae_matrix enqueuedjac;
ae_vector sortedstp;
ae_vector sortedidx;
ae_int_t sortedcnt;
double probingstp;
ae_vector probingf;
ae_int_t probingnvalues;
double probingstepmax;
double probingstepscale;
ae_int_t probingnstepsstored;
ae_vector probingsteps;
ae_matrix probingvalues;
ae_matrix probingslopes;
rcommstate probingrcomm;
ae_bool linesearchspoiled;
ae_bool linesearchstarted;
double nonc0currentrating;
double nonc1currentrating;
ae_bool badgradhasxj;
optguardreport rep;
double nonc0strrating;
double nonc0lngrating;
optguardnonc0report nonc0strrep;
optguardnonc0report nonc0lngrep;
double nonc1test0strrating;
double nonc1test0lngrating;
optguardnonc1test0report nonc1test0strrep;
optguardnonc1test0report nonc1test0lngrep;
double nonc1test1strrating;
double nonc1test1lngrating;
optguardnonc1test1report nonc1test1strrep;
optguardnonc1test1report nonc1test1lngrep;
ae_bool needfij;
ae_vector x;
ae_vector fi;
ae_matrix j;
rcommstate rstateg0;
ae_vector xbase;
ae_vector fbase;
ae_vector fm;
ae_vector fc;
ae_vector fp;
ae_vector jm;
ae_vector jc;
ae_vector jp;
ae_matrix jbaseusr;
ae_matrix jbasenum;
ae_vector stp;
ae_vector bufr;
ae_vector f;
ae_vector g;
ae_vector deltax;
ae_vector tmpidx;
ae_vector bufi;
ae_vector xu;
ae_vector du;
ae_vector f0;
ae_matrix j0;
} smoothnessmonitor;
#endif
#if defined(AE_COMPILE_SNNLS) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t ns;
ae_int_t nd;
ae_int_t nr;
ae_matrix densea;
ae_vector b;
ae_vector nnc;
double debugflops;
ae_int_t debugmaxinnerits;
ae_vector xn;
ae_vector xp;
ae_matrix tmpca;
ae_matrix tmplq;
ae_matrix trda;
ae_vector trdd;
ae_vector crb;
ae_vector g;
ae_vector d;
ae_vector dx;
ae_vector diagaa;
ae_vector cb;
ae_vector cx;
ae_vector cborg;
ae_vector tmpcholesky;
ae_vector r;
ae_vector regdiag;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
ae_vector rdtmprowmap;
} snnlssolver;
#endif
#if defined(AE_COMPILE_SACTIVESETS) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t algostate;
ae_vector xc;
ae_bool hasxc;
ae_vector s;
ae_vector h;
ae_vector cstatus;
ae_bool basisisready;
ae_matrix sdensebatch;
ae_matrix pdensebatch;
ae_matrix idensebatch;
ae_int_t densebatchsize;
ae_vector sparsebatch;
ae_int_t sparsebatchsize;
ae_int_t basisage;
ae_bool feasinitpt;
ae_bool constraintschanged;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector bndl;
ae_vector bndu;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
ae_vector mtnew;
ae_vector mtx;
ae_vector mtas;
ae_vector cdtmp;
ae_vector corrtmp;
ae_vector unitdiagonal;
snnlssolver solver;
ae_vector scntmp;
ae_vector tmp0;
ae_vector tmpfeas;
ae_matrix tmpm0;
ae_vector rctmps;
ae_vector rctmpg;
ae_vector rctmprightpart;
ae_matrix rctmpdense0;
ae_matrix rctmpdense1;
ae_vector rctmpisequality;
ae_vector rctmpconstraintidx;
ae_vector rctmplambdas;
ae_matrix tmpbasis;
ae_vector tmpnormestimates;
ae_vector tmpreciph;
ae_vector tmpprodp;
ae_vector tmpprods;
ae_vector tmpcp;
ae_vector tmpcs;
ae_vector tmpci;
} sactiveset;
#endif
#if defined(AE_COMPILE_QQPSOLVER) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double epsg;
double epsf;
double epsx;
ae_int_t maxouterits;
ae_bool cgphase;
ae_bool cnphase;
ae_int_t cgminits;
ae_int_t cgmaxits;
ae_int_t cnmaxupdates;
ae_int_t sparsesolver;
} qqpsettings;
typedef struct
{
ae_int_t n;
ae_int_t akind;
ae_matrix densea;
sparsematrix sparsea;
ae_bool sparseupper;
double absamax;
double absasum;
double absasum2;
ae_vector b;
ae_vector bndl;
ae_vector bndu;
ae_vector havebndl;
ae_vector havebndu;
ae_vector xs;
ae_vector xf;
ae_vector gc;
ae_vector xp;
ae_vector dc;
ae_vector dp;
ae_vector cgc;
ae_vector cgp;
sactiveset sas;
ae_vector activated;
ae_int_t nfree;
ae_int_t cnmodelage;
ae_matrix densez;
sparsematrix sparsecca;
ae_vector yidx;
ae_vector regdiag;
ae_vector regx0;
ae_vector tmpcn;
ae_vector tmpcni;
ae_vector tmpcnb;
ae_vector tmp0;
ae_vector tmp1;
ae_vector stpbuf;
sparsebuffers sbuf;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repncupdates;
} qqpbuffers;
#endif
#if defined(AE_COMPILE_LPQPSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_VIPMSOLVER) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t m;
ae_vector x;
ae_vector g;
ae_vector w;
ae_vector t;
ae_vector p;
ae_vector y;
ae_vector z;
ae_vector v;
ae_vector s;
ae_vector q;
} vipmvars;
typedef struct
{
ae_int_t n;
ae_int_t nmain;
double regeps;
double epsp;
double epsd;
double epsgap;
ae_bool islinear;
ae_vector scl;
ae_vector invscl;
ae_vector xorigin;
double targetscale;
ae_vector c;
ae_matrix denseh;
sparsematrix sparseh;
ae_int_t hkind;
ae_vector bndl;
ae_vector bndu;
ae_vector rawbndl;
ae_vector rawbndu;
ae_vector hasbndl;
ae_vector hasbndu;
ae_matrix denseafull;
ae_matrix denseamain;
sparsematrix sparseafull;
sparsematrix sparseamain;
sparsematrix combinedaslack;
ae_vector ascales;
ae_vector b;
ae_vector r;
ae_vector hasr;
ae_int_t mdense;
ae_int_t msparse;
vipmvars current;
vipmvars trial;
vipmvars deltaaff;
vipmvars deltacorr;
double errp2;
double errd2;
double errpinf;
double errdinf;
ae_int_t repiterationscount;
ae_int_t repncholesky;
ae_int_t factorizationtype;
ae_bool factorizationpoweredup;
ae_bool factorizationpresent;
ae_vector diagginvz;
ae_vector diagzinvg;
ae_vector diagtinvs;
ae_vector diagsinvt;
ae_vector diagvinvw;
ae_vector diagpinvq;
ae_vector diagqinvp;
ae_vector diagd;
ae_vector diage;
ae_matrix factdensehaug;
ae_vector factdh;
ae_vector factdz;
ae_vector factinvdz;
ae_vector facteffectivee;
sparsematrix factsparsekkttmpl;
sparsematrix factsparsekkt;
ae_vector factsparsekktpivp;
ae_vector factsparsekktpivq;
ae_vector rhsrho;
ae_vector rhsnu;
ae_vector rhstau;
ae_vector rhsalpha;
ae_vector rhssigma;
ae_vector rhsbeta;
ae_vector rhsgammaz;
ae_vector rhsgammas;
ae_vector rhsgammaw;
ae_vector rhsgammaq;
ae_vector rhsalphacap;
ae_vector rhsbetacap;
ae_vector rhsnucap;
ae_vector rhstaucap;
ae_vector deltaxy;
ae_vector tmphx;
ae_vector tmpax;
ae_vector tmpaty;
ae_vector dummyr;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
ae_matrix tmpr2;
ae_vector evalprogressg;
ae_vector tmpi;
sparsematrix tmpsparse0;
sparsematrix tmpsparse1;
} vipmstate;
#endif
#if defined(AE_COMPILE_NLCSQP) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t algokind;
vipmstate ipmsolver;
ae_vector curb;
ae_vector curbndl;
ae_vector curbndu;
ae_vector cural;
ae_vector curau;
sparsematrix sparserawlc;
sparsematrix sparseefflc;
ae_vector d0;
ae_matrix h;
ae_matrix densedummy;
sparsematrix sparsedummy;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
ae_vector sk;
ae_vector yk;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector hasal;
ae_vector hasau;
ae_matrix activea;
ae_vector activerhs;
ae_vector activeidx;
ae_int_t activesetsize;
} minsqpsubsolver;
typedef struct
{
ae_vector sclagtmp0;
ae_vector sclagtmp1;
} minsqptmplagrangian;
typedef struct
{
ae_vector mftmp0;
} minsqptmpmerit;
typedef struct
{
ae_int_t n;
ae_int_t nec;
ae_int_t nic;
ae_int_t nlec;
ae_int_t nlic;
ae_vector d;
ae_vector dx;
ae_vector stepkx;
ae_vector stepkxc;
ae_vector stepkxn;
ae_vector stepkfi;
ae_vector stepkfic;
ae_vector stepkfin;
ae_matrix stepkj;
ae_matrix stepkjc;
ae_matrix stepkjn;
ae_vector lagmult;
ae_vector dummylagmult;
minsqptmpmerit tmpmerit;
minsqptmplagrangian tmplagrangianfg;
ae_vector stepklaggrad;
ae_vector stepknlaggrad;
ae_int_t status;
rcommstate rmeritphasestate;
} minsqpmeritphasestate;
typedef struct
{
ae_int_t n;
ae_int_t nec;
ae_int_t nic;
ae_int_t nlec;
ae_int_t nlic;
ae_vector s;
ae_matrix scaledcleic;
ae_vector lcsrcidx;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector scaledbndl;
ae_vector scaledbndu;
double epsx;
ae_int_t maxits;
ae_vector x;
ae_vector fi;
ae_matrix j;
double f;
ae_bool needfij;
ae_bool xupdated;
minsqpmeritphasestate meritstate;
double trustrad;
ae_int_t fstagnationcnt;
ae_vector step0x;
ae_vector stepkx;
ae_vector backupx;
ae_vector step0fi;
ae_vector stepkfi;
ae_vector backupfi;
ae_matrix step0j;
ae_matrix stepkj;
ae_bool haslagmult;
ae_vector meritlagmult;
ae_vector dummylagmult;
ae_vector fscales;
minsqpsubsolver subsolver;
minsqptmpmerit tmpmerit;
ae_int_t repsimplexiterations;
ae_int_t repsimplexiterations1;
ae_int_t repsimplexiterations2;
ae_int_t repsimplexiterations3;
ae_int_t repiterationscount;
ae_int_t repterminationtype;
double repbcerr;
ae_int_t repbcidx;
double replcerr;
ae_int_t replcidx;
double repnlcerr;
ae_int_t repnlcidx;
rcommstate rstate;
} minsqpstate;
#endif
#if defined(AE_COMPILE_MINLBFGS) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t m;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_vector s;
double diffstep;
ae_int_t nfev;
ae_int_t mcstage;
ae_int_t k;
ae_int_t q;
ae_int_t p;
ae_vector rho;
ae_matrix yk;
ae_matrix sk;
ae_vector xp;
ae_vector theta;
ae_vector d;
double stp;
ae_vector work;
double fold;
double trimthreshold;
ae_vector xbase;
ae_int_t prectype;
double gammak;
ae_matrix denseh;
ae_vector diagh;
ae_vector precc;
ae_vector precd;
ae_matrix precw;
ae_int_t preck;
precbuflbfgs precbuf;
precbuflowrank lowrankbuf;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
ae_vector autobuf;
ae_vector invs;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool userterminationneeded;
double teststep;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repterminationtype;
linminstate lstate;
ae_int_t smoothnessguardlevel;
smoothnessmonitor smonitor;
ae_vector lastscaleused;
} minlbfgsstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t terminationtype;
} minlbfgsreport;
#endif
#if defined(AE_COMPILE_QPDENSEAULSOLVER) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double epsx;
ae_int_t outerits;
double rho;
} qpdenseaulsettings;
typedef struct
{
ae_vector nulc;
ae_matrix sclsfta;
ae_vector sclsftb;
ae_vector sclsfthasbndl;
ae_vector sclsfthasbndu;
ae_vector sclsftbndl;
ae_vector sclsftbndu;
ae_vector sclsftxc;
ae_matrix sclsftcleic;
ae_vector cidx;
ae_vector cscales;
ae_matrix exa;
ae_vector exb;
ae_vector exxc;
ae_vector exbndl;
ae_vector exbndu;
ae_vector exscale;
ae_vector exxorigin;
qqpsettings qqpsettingsuser;
qqpbuffers qqpbuf;
ae_vector nulcest;
ae_vector tmpg;
ae_vector tmp0;
ae_matrix tmp2;
ae_vector modelg;
ae_vector d;
ae_vector deltax;
convexquadraticmodel dummycqm;
sparsematrix dummysparse;
ae_matrix qrkkt;
ae_vector qrrightpart;
ae_vector qrtau;
ae_vector qrsv0;
ae_vector qrsvx1;
ae_vector nicerr;
ae_vector nicnact;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repnwrkchanges;
ae_int_t repnwrk0;
ae_int_t repnwrk1;
ae_int_t repnwrkf;
ae_int_t repnmv;
} qpdenseaulbuffers;
#endif
#if defined(AE_COMPILE_MINBLEIC) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t nmain;
ae_int_t nslack;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
ae_bool drep;
double stpmax;
double diffstep;
sactiveset sas;
ae_vector s;
ae_int_t prectype;
ae_vector diagh;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool lsstart;
ae_bool steepestdescentstep;
ae_bool boundedstep;
ae_bool userterminationneeded;
rcommstate rstate;
ae_vector ugc;
ae_vector cgc;
ae_vector xn;
ae_vector ugn;
ae_vector cgn;
ae_vector xp;
double fc;
double fn;
double fp;
ae_vector d;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
double lastgoodstep;
double lastscaledgoodstep;
double maxscaledgrad;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector bndl;
ae_vector bndu;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
double repdebugeqerr;
double repdebugfs;
double repdebugff;
double repdebugdx;
ae_int_t repdebugfeasqpits;
ae_int_t repdebugfeasgpaits;
ae_vector xstart;
snnlssolver solver;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
double xm1;
double xp1;
double gm1;
double gp1;
ae_int_t cidx;
double cval;
ae_vector tmpprec;
ae_vector tmp0;
ae_int_t nfev;
ae_int_t mcstage;
double stp;
double curstpmax;
double activationstep;
ae_vector work;
linminstate lstate;
double trimthreshold;
ae_int_t nonmonotoniccnt;
ae_matrix bufyk;
ae_matrix bufsk;
ae_vector bufrho;
ae_vector buftheta;
ae_int_t bufsize;
double teststep;
ae_int_t smoothnessguardlevel;
smoothnessmonitor smonitor;
ae_vector lastscaleused;
ae_vector invs;
} minbleicstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
double debugeqerr;
double debugfs;
double debugff;
double debugdx;
ae_int_t debugfeasqpits;
ae_int_t debugfeasgpaits;
ae_int_t inneriterationscount;
ae_int_t outeriterationscount;
} minbleicreport;
#endif
#if defined(AE_COMPILE_QPBLEICSOLVER) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
} qpbleicsettings;
typedef struct
{
minbleicstate solver;
minbleicreport solverrep;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpi;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
} qpbleicbuffers;
#endif
#if defined(AE_COMPILE_MINQP) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
qqpsettings qqpsettingsuser;
qpbleicsettings qpbleicsettingsuser;
qpdenseaulsettings qpdenseaulsettingsuser;
double veps;
ae_bool dbgskipconstraintnormalization;
ae_int_t algokind;
ae_int_t akind;
convexquadraticmodel a;
sparsematrix sparsea;
ae_bool sparseaupper;
double absamax;
double absasum;
double absasum2;
ae_vector b;
ae_vector bndl;
ae_vector bndu;
ae_int_t stype;
ae_vector s;
ae_vector havebndl;
ae_vector havebndu;
ae_vector xorigin;
ae_vector startx;
ae_bool havex;
ae_matrix densec;
sparsematrix sparsec;
ae_vector cl;
ae_vector cu;
ae_int_t mdense;
ae_int_t msparse;
ae_vector xs;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repnmv;
ae_int_t repterminationtype;
ae_vector replagbc;
ae_vector replaglc;
ae_vector effectives;
ae_vector tmp0;
ae_matrix ecleic;
ae_vector elaglc;
ae_vector elagmlt;
ae_vector elagidx;
ae_matrix dummyr2;
sparsematrix dummysparse;
ae_matrix tmpr2;
ae_bool qpbleicfirstcall;
qpbleicbuffers qpbleicbuf;
qqpbuffers qqpbuf;
qpdenseaulbuffers qpdenseaulbuf;
vipmstate vsolver;
} minqpstate;
typedef struct
{
ae_int_t inneriterationscount;
ae_int_t outeriterationscount;
ae_int_t nmv;
ae_int_t ncholesky;
ae_int_t terminationtype;
ae_vector lagbc;
ae_vector laglc;
} minqpreport;
#endif
#if defined(AE_COMPILE_REVISEDDUALSIMPLEX) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double pivottol;
double perturbmag;
ae_int_t maxtrfage;
ae_int_t trftype;
ae_int_t ratiotest;
ae_int_t pricing;
ae_int_t shifting;
} dualsimplexsettings;
typedef struct
{
ae_int_t ns;
ae_int_t m;
ae_vector idx;
ae_vector nidx;
ae_vector isbasic;
ae_int_t trftype;
ae_bool isvalidtrf;
ae_int_t trfage;
ae_matrix denselu;
sparsematrix sparsel;
sparsematrix sparseu;
sparsematrix sparseut;
ae_vector rowpermbwd;
ae_vector colpermbwd;
ae_vector densepfieta;
ae_vector densemu;
ae_vector rk;
ae_vector dk;
ae_vector dseweights;
ae_bool dsevalid;
double eminu;
ae_vector wtmp0;
ae_vector wtmp1;
ae_vector wtmp2;
ae_vector nrs;
ae_vector tcinvidx;
ae_matrix denselu2;
ae_vector densep2;
ae_vector densep2c;
sparsematrix sparselu1;
sparsematrix sparselu2;
sluv2buffer lubuf2;
ae_vector tmpi;
ae_vector utmp0;
ae_vector utmpi;
sparsematrix sparseludbg;
} dualsimplexbasis;
typedef struct
{
ae_int_t ns;
ae_int_t m;
ae_vector rawc;
ae_vector bndl;
ae_vector bndu;
ae_vector bndt;
ae_vector xa;
ae_vector d;
ae_int_t state;
ae_vector xb;
ae_vector bndlb;
ae_vector bndub;
ae_vector bndtb;
ae_vector effc;
ae_vector colscales;
} dualsimplexsubproblem;
typedef struct
{
ae_vector varscales;
ae_vector rowscales;
ae_vector rawbndl;
ae_vector rawbndu;
ae_int_t ns;
ae_int_t m;
sparsematrix a;
sparsematrix at;
dualsimplexbasis basis;
dualsimplexsubproblem primary;
dualsimplexsubproblem phase1;
dualsimplexsubproblem phase3;
ae_vector repx;
ae_vector repy;
ae_vector repdx;
ae_vector repstats;
double repf;
double repprimalerror;
double repdualerror;
ae_int_t repterminationtype;
ae_int_t repiterationscount;
ae_int_t repiterationscount1;
ae_int_t repiterationscount2;
ae_int_t repiterationscount3;
ae_vector possibleflips;
ae_int_t possibleflipscnt;
ae_vector dfctmp0;
ae_vector dfctmp1;
ae_vector dfctmp2;
ae_vector ustmpi;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
ae_vector alphar;
ae_vector rhor;
ae_vector tau;
ae_vector alphaq;
ae_vector alphaqim;
ae_vector eligibleset;
ae_vector harrisset;
} dualsimplexstate;
#endif
#if defined(AE_COMPILE_MINLP) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t algokind;
ae_vector s;
ae_vector c;
ae_vector bndl;
ae_vector bndu;
ae_int_t m;
sparsematrix a;
ae_vector al;
ae_vector au;
ae_vector xs;
ae_vector ys;
ae_vector cs;
double repf;
double repprimalerror;
double repdualerror;
ae_int_t repiterationscount;
ae_int_t repterminationtype;
dualsimplexstate dss;
ae_vector adddtmpi;
ae_vector adddtmpr;
} minlpstate;
typedef struct
{
double f;
ae_vector y;
ae_vector stats;
double primalerror;
double dualerror;
ae_int_t iterationscount;
ae_int_t terminationtype;
} minlpreport;
#endif
#if defined(AE_COMPILE_NLCSLP) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
dualsimplexstate dss;
dualsimplexsettings dsssettings;
dualsimplexbasis lastbasis;
ae_bool basispresent;
ae_matrix curd;
ae_int_t curdcnt;
ae_vector curb;
ae_vector curbndl;
ae_vector curbndu;
ae_vector cural;
ae_vector curau;
sparsematrix sparserawlc;
sparsematrix sparseefflc;
ae_int_t hessiantype;
ae_matrix h;
ae_matrix curhd;
ae_matrix densedummy;
sparsematrix sparsedummy;
ae_vector tmp0;
ae_vector tmp1;
ae_vector sk;
ae_vector yk;
} minslpsubsolver;
typedef struct
{
ae_vector sclagtmp0;
ae_vector sclagtmp1;
} minslptmplagrangian;
typedef struct
{
ae_vector mftmp0;
} minslptmpmerit;
typedef struct
{
ae_bool usecorrection;
ae_vector d;
ae_vector dx;
ae_vector stepkxc;
ae_vector stepkxn;
ae_vector stepkfic;
ae_vector stepkfin;
ae_matrix stepkjc;
ae_matrix stepkjn;
ae_vector dummylagmult;
minslptmpmerit tmpmerit;
rcommstate rphase13state;
} minslpphase13state;
typedef struct
{
ae_vector stepkxn;
ae_vector stepkxc;
ae_vector stepkfin;
ae_vector stepkfic;
ae_matrix stepkjn;
ae_matrix stepkjc;
ae_vector stepklaggrad;
ae_vector stepknlaggrad;
ae_vector stepknlagmult;
ae_vector meritlagmult;
minslptmplagrangian tmplagrangianfg;
double lastlcerr;
ae_int_t lastlcidx;
double lastnlcerr;
ae_int_t lastnlcidx;
ae_vector tmp0;
ae_vector d;
linminstate mcstate;
minslptmpmerit tmpmerit;
rcommstate rphase2state;
} minslpphase2state;
typedef struct
{
ae_int_t n;
ae_int_t nec;
ae_int_t nic;
ae_int_t nlec;
ae_int_t nlic;
ae_vector s;
ae_matrix scaledcleic;
ae_vector lcsrcidx;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector scaledbndl;
ae_vector scaledbndu;
double epsx;
ae_int_t maxits;
ae_int_t hessiantype;
ae_vector x;
ae_vector fi;
ae_matrix j;
double f;
ae_bool needfij;
ae_bool xupdated;
minslpphase13state state13;
minslpphase2state state2;
double trustrad;
ae_int_t lpfailurecnt;
ae_int_t fstagnationcnt;
ae_vector step0x;
ae_vector stepkx;
ae_vector backupx;
ae_vector step0fi;
ae_vector stepkfi;
ae_vector backupfi;
ae_matrix step0j;
ae_matrix stepkj;
ae_matrix backupj;
ae_vector meritlagmult;
ae_vector dummylagmult;
ae_vector fscales;
ae_vector meritfunctionhistory;
ae_int_t historylen;
minslpsubsolver subsolver;
minslptmpmerit tmpmerit;
ae_int_t repsimplexiterations;
ae_int_t repsimplexiterations1;
ae_int_t repsimplexiterations2;
ae_int_t repsimplexiterations3;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repterminationtype;
double repbcerr;
ae_int_t repbcidx;
double replcerr;
ae_int_t replcidx;
double repnlcerr;
ae_int_t repnlcidx;
rcommstate rstate;
} minslpstate;
#endif
#if defined(AE_COMPILE_MINNLC) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double stabilizingpoint;
double initialinequalitymultiplier;
ae_int_t solvertype;
ae_int_t prectype;
ae_int_t updatefreq;
double rho;
ae_int_t n;
double epsx;
ae_int_t maxits;
ae_int_t aulitscnt;
ae_bool xrep;
double stpmax;
double diffstep;
double teststep;
ae_vector s;
ae_vector bndl;
ae_vector bndu;
ae_vector hasbndl;
ae_vector hasbndu;
ae_int_t nec;
ae_int_t nic;
ae_matrix cleic;
ae_vector lcsrcidx;
ae_int_t ng;
ae_int_t nh;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
rcommstate rstate;
rcommstate rstateaul;
rcommstate rstateslp;
ae_vector scaledbndl;
ae_vector scaledbndu;
ae_matrix scaledcleic;
ae_vector xc;
ae_vector xstart;
ae_vector xbase;
ae_vector fbase;
ae_vector dfbase;
ae_vector fm2;
ae_vector fm1;
ae_vector fp1;
ae_vector fp2;
ae_vector dfm1;
ae_vector dfp1;
ae_vector bufd;
ae_vector bufc;
ae_vector tmp0;
ae_matrix bufw;
ae_matrix bufz;
ae_vector xk;
ae_vector xk1;
ae_vector gk;
ae_vector gk1;
double gammak;
ae_bool xkpresent;
minlbfgsstate auloptimizer;
minlbfgsreport aulreport;
ae_vector nubc;
ae_vector nulc;
ae_vector nunlc;
ae_bool userterminationneeded;
minslpstate slpsolverstate;
minsqpstate sqpsolverstate;
ae_int_t smoothnessguardlevel;
smoothnessmonitor smonitor;
ae_vector lastscaleused;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repterminationtype;
double repbcerr;
ae_int_t repbcidx;
double replcerr;
ae_int_t replcidx;
double repnlcerr;
ae_int_t repnlcidx;
ae_int_t repdbgphase0its;
} minnlcstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t terminationtype;
double bcerr;
ae_int_t bcidx;
double lcerr;
ae_int_t lcidx;
double nlcerr;
ae_int_t nlcidx;
ae_int_t dbgphase0its;
} minnlcreport;
#endif
#if defined(AE_COMPILE_MINBC) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t nmain;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
double diffstep;
ae_vector s;
ae_int_t prectype;
ae_vector diagh;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool userterminationneeded;
rcommstate rstate;
ae_vector xc;
ae_vector ugc;
ae_vector cgc;
ae_vector xn;
ae_vector ugn;
ae_vector cgn;
ae_vector xp;
double fc;
double fn;
double fp;
ae_vector d;
double lastscaledgoodstep;
ae_vector hasbndl;
ae_vector hasbndu;
ae_vector bndl;
ae_vector bndu;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
ae_vector xstart;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
double xm1;
double xp1;
double gm1;
double gp1;
ae_vector tmpprec;
ae_vector tmp0;
ae_int_t nfev;
ae_int_t mcstage;
double stp;
double curstpmax;
ae_vector work;
linminstate lstate;
double trimthreshold;
ae_int_t nonmonotoniccnt;
ae_matrix bufyk;
ae_matrix bufsk;
ae_vector bufrho;
ae_vector buftheta;
ae_int_t bufsize;
double teststep;
ae_int_t smoothnessguardlevel;
smoothnessmonitor smonitor;
ae_vector lastscaleused;
ae_vector invs;
} minbcstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
} minbcreport;
#endif
#if defined(AE_COMPILE_MINNS) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
double fc;
double fn;
ae_vector xc;
ae_vector xn;
ae_vector x0;
ae_vector gc;
ae_vector d;
ae_matrix uh;
ae_matrix ch;
ae_matrix rk;
ae_vector invutc;
ae_vector tmp0;
ae_vector tmpidx;
ae_vector tmpd;
ae_vector tmpc;
ae_vector tmplambdas;
ae_matrix tmpc2;
ae_vector tmpb;
snnlssolver nnls;
} minnsqp;
typedef struct
{
ae_int_t solvertype;
ae_int_t n;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double diffstep;
ae_vector s;
ae_vector bndl;
ae_vector bndu;
ae_vector hasbndl;
ae_vector hasbndu;
ae_int_t nec;
ae_int_t nic;
ae_matrix cleic;
ae_int_t ng;
ae_int_t nh;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
rcommstate rstate;
rcommstate rstateags;
hqrndstate agsrs;
double agsradius;
ae_int_t agssamplesize;
double agsraddecay;
double agsalphadecay;
double agsdecrease;
double agsinitstp;
double agsstattold;
double agsshortstpabs;
double agsshortstprel;
double agsshortf;
ae_int_t agsshortlimit;
double agsrhononlinear;
ae_int_t agsminupdate;
ae_int_t agsmaxraddecays;
ae_int_t agsmaxbacktrack;
ae_int_t agsmaxbacktracknonfull;
double agspenaltylevel;
double agspenaltyincrease;
ae_vector xstart;
ae_vector xc;
ae_vector xn;
ae_vector grs;
ae_vector d;
ae_vector colmax;
ae_vector diagh;
ae_vector signmin;
ae_vector signmax;
ae_bool userterminationneeded;
ae_vector scaledbndl;
ae_vector scaledbndu;
ae_matrix scaledcleic;
ae_vector rholinear;
ae_matrix samplex;
ae_matrix samplegm;
ae_matrix samplegmbc;
ae_vector samplef;
ae_vector samplef0;
minnsqp nsqp;
ae_vector tmp0;
ae_vector tmp1;
ae_matrix tmp2;
ae_vector tmp3;
ae_vector xbase;
ae_vector fp;
ae_vector fm;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repfuncidx;
ae_int_t repterminationtype;
double replcerr;
double repnlcerr;
ae_int_t dbgncholesky;
} minnsstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
double cerr;
double lcerr;
double nlcerr;
ae_int_t terminationtype;
ae_int_t varidx;
ae_int_t funcidx;
} minnsreport;
#endif
#if defined(AE_COMPILE_MINCOMP) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_int_t cgtype;
ae_int_t k;
ae_int_t nfev;
ae_int_t mcstage;
ae_vector bndl;
ae_vector bndu;
ae_int_t curalgo;
ae_int_t acount;
double mu;
double finit;
double dginit;
ae_vector ak;
ae_vector xk;
ae_vector dk;
ae_vector an;
ae_vector xn;
ae_vector dn;
ae_vector d;
double fold;
double stp;
ae_vector work;
ae_vector yk;
ae_vector gc;
double laststep;
ae_vector x;
double f;
ae_vector g;
ae_bool needfg;
ae_bool xupdated;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repterminationtype;
ae_int_t debugrestartscount;
linminstate lstate;
double betahs;
double betady;
} minasastate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t terminationtype;
ae_int_t activeconstraints;
} minasareport;
#endif
#if defined(AE_COMPILE_MINCG) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
double epsg;
double epsf;
double epsx;
ae_int_t maxits;
double stpmax;
double suggestedstep;
ae_bool xrep;
ae_bool drep;
ae_int_t cgtype;
ae_int_t prectype;
ae_vector diagh;
ae_vector diaghl2;
ae_matrix vcorr;
ae_int_t vcnt;
ae_vector s;
double diffstep;
ae_int_t nfev;
ae_int_t mcstage;
ae_int_t k;
ae_vector xk;
ae_vector dk;
ae_vector xn;
ae_vector dn;
ae_vector d;
double fold;
double stp;
double curstpmax;
ae_vector yk;
double lastgoodstep;
double lastscaledstep;
ae_int_t mcinfo;
ae_bool innerresetneeded;
ae_bool terminationneeded;
double trimthreshold;
ae_vector xbase;
ae_int_t rstimer;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
ae_bool algpowerup;
ae_bool lsstart;
ae_bool lsend;
ae_bool userterminationneeded;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repterminationtype;
ae_int_t debugrestartscount;
linminstate lstate;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
double betahs;
double betady;
ae_vector work0;
ae_vector work1;
ae_vector invs;
double teststep;
ae_int_t smoothnessguardlevel;
smoothnessmonitor smonitor;
ae_vector lastscaleused;
} mincgstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t terminationtype;
} mincgreport;
#endif
#if defined(AE_COMPILE_MINLM) || !defined(AE_PARTIAL_BUILD)
typedef struct
{
ae_int_t n;
ae_int_t m;
double stpmax;
ae_int_t modelage;
ae_int_t maxmodelage;
ae_bool hasfi;
double epsx;
ae_vector x;
double f;
ae_vector fi;
ae_bool needf;
ae_bool needfi;
double fbase;
ae_vector modeldiag;
ae_vector xbase;
ae_vector fibase;
ae_vector bndl;
ae_vector bndu;
ae_vector havebndl;
ae_vector havebndu;
ae_vector s;
rcommstate rstate;
ae_vector xdir;
ae_vector choleskybuf;
ae_vector tmp0;
ae_vector tmpct;
double actualdecrease;
double predicteddecrease;
minqpstate qpstate;
minqpreport qprep;
sparsematrix tmpsp;
} minlmstepfinder;
typedef struct
{
ae_int_t n;
ae_int_t m;
double diffstep;
double epsx;
ae_int_t maxits;
ae_bool xrep;
double stpmax;
ae_int_t maxmodelage;
ae_bool makeadditers;
ae_vector x;
double f;
ae_vector fi;
ae_matrix j;
ae_matrix h;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool needfgh;
ae_bool needfij;
ae_bool needfi;
ae_bool xupdated;
ae_bool userterminationneeded;
ae_int_t algomode;
ae_bool hasf;
ae_bool hasfi;
ae_bool hasg;
ae_vector xbase;
double fbase;
ae_vector fibase;
ae_vector gbase;
ae_matrix quadraticmodel;
ae_vector bndl;
ae_vector bndu;
ae_vector havebndl;
ae_vector havebndu;
ae_vector s;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
double lambdav;
double nu;
ae_int_t modelage;
ae_vector xnew;
ae_vector xdir;
ae_vector deltax;
ae_vector deltaf;
ae_bool deltaxready;
ae_bool deltafready;
smoothnessmonitor smonitor;
double teststep;
ae_vector lastscaleused;
ae_int_t repiterationscount;
ae_int_t repterminationtype;
ae_int_t repnfunc;
ae_int_t repnjac;
ae_int_t repngrad;
ae_int_t repnhess;
ae_int_t repncholesky;
rcommstate rstate;
ae_vector choleskybuf;
ae_vector tmp0;
double actualdecrease;
double predicteddecrease;
double xm1;
double xp1;
ae_vector fm1;
ae_vector fp1;
ae_vector fc1;
ae_vector gm1;
ae_vector gp1;
ae_vector gc1;
minlbfgsstate internalstate;
minlbfgsreport internalrep;
minqpstate qpstate;
minqpreport qprep;
minlmstepfinder finderstate;
} minlmstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t terminationtype;
ae_int_t nfunc;
ae_int_t njac;
ae_int_t ngrad;
ae_int_t nhess;
ae_int_t ncholesky;
} minlmreport;
#endif
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{
#if defined(AE_COMPILE_CQMODELS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_OPTGUARDAPI) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This structure is used to store OptGuard report, i.e. report on the
properties of the nonlinear function being optimized with ALGLIB.
After you tell your optimizer to activate OptGuard this technology starts
to silently monitor function values and gradients/Jacobians being passed
all around during your optimization session. Depending on specific set of
checks enabled OptGuard may perform additional function evaluations (say,
about 3*N evaluations if you want to check analytic gradient for errors).
Upon discovering that something strange happens (function values and/or
gradient components change too sharply and/or unexpectedly) OptGuard sets
one of the "suspicion flags" (without interrupting optimization session).
After optimization is done, you can examine OptGuard report.
Following report fields can be set:
* nonc0suspected
* nonc1suspected
* badgradsuspected
=== WHAT CAN BE DETECTED WITH OptGuard INTEGRITY CHECKER =================
Following types of errors in your target function (constraints) can be
caught:
a) discontinuous functions ("non-C0" part of the report)
b) functions with discontinuous derivative ("non-C1" part of the report)
c) errors in the analytic gradient provided by user
These types of errors result in optimizer stopping well before reaching
solution (most often - right after encountering discontinuity).
Type A errors are usually coding errors during implementation of the
target function. Most "normal" problems involve continuous functions, and
anyway you can't reliably optimize discontinuous function.
Type B errors are either coding errors or (in case code itself is correct)
evidence of the fact that your problem is an "incorrect" one. Most
optimizers (except for ones provided by MINNS subpackage) do not support
nonsmooth problems.
Type C errors are coding errors which often prevent optimizer from making
even one step or result in optimizing stopping too early, as soon as
actual descent direction becomes too different from one suggested by user-
supplied gradient.
=== WHAT IS REPORTED =====================================================
Following set of report fields deals with discontinuous target functions,
ones not belonging to C0 continuity class:
* nonc0suspected - is a flag which is set upon discovering some indication
of the discontinuity. If this flag is false, the rest of "non-C0" fields
should be ignored
* nonc0fidx - is an index of the function (0 for target function, 1 or
higher for nonlinear constraints) which is suspected of being "non-C0"
* nonc0lipshitzc - a Lipchitz constant for a function which was suspected
of being non-continuous.
* nonc0test0positive - set to indicate specific test which detected
continuity violation (test #0)
Following set of report fields deals with discontinuous gradient/Jacobian,
i.e. with functions violating C1 continuity:
* nonc1suspected - is a flag which is set upon discovering some indication
of the discontinuity. If this flag is false, the rest of "non-C1" fields
should be ignored
* nonc1fidx - is an index of the function (0 for target function, 1 or
higher for nonlinear constraints) which is suspected of being "non-C1"
* nonc1lipshitzc - a Lipchitz constant for a function gradient which was
suspected of being non-smooth.
* nonc1test0positive - set to indicate specific test which detected
continuity violation (test #0)
* nonc1test1positive - set to indicate specific test which detected
continuity violation (test #1)
Following set of report fields deals with errors in the gradient:
* badgradsuspected - is a flad which is set upon discovering an error in
the analytic gradient supplied by user
* badgradfidx - index of the function with bad gradient (0 for target
function, 1 or higher for nonlinear constraints)
* badgradvidx - index of the variable
* badgradxbase - location where Jacobian is tested
* following matrices store user-supplied Jacobian and its numerical
differentiation version (which is assumed to be free from the coding
errors), both of them computed near the initial point:
* badgraduser, an array[K,N], analytic Jacobian supplied by user
* badgradnum, an array[K,N], numeric Jacobian computed by ALGLIB
Here K is a total number of nonlinear functions (target + nonlinear
constraints), N is a variable number.
The element of badgraduser[] with index [badgradfidx,badgradvidx] is
assumed to be wrong.
More detailed error log can be obtained from optimizer by explicitly
requesting reports for tests C0.0, C1.0, C1.1.
-- ALGLIB --
Copyright 19.11.2018 by Bochkanov Sergey
*************************************************************************/
class _optguardreport_owner
{
public:
_optguardreport_owner();
_optguardreport_owner(const _optguardreport_owner &rhs);
_optguardreport_owner& operator=(const _optguardreport_owner &rhs);
virtual ~_optguardreport_owner();
alglib_impl::optguardreport* c_ptr();
alglib_impl::optguardreport* c_ptr() const;
protected:
alglib_impl::optguardreport *p_struct;
};
class optguardreport : public _optguardreport_owner
{
public:
optguardreport();
optguardreport(const optguardreport &rhs);
optguardreport& operator=(const optguardreport &rhs);
virtual ~optguardreport();
ae_bool &nonc0suspected;
ae_bool &nonc0test0positive;
ae_int_t &nonc0fidx;
double &nonc0lipschitzc;
ae_bool &nonc1suspected;
ae_bool &nonc1test0positive;
ae_bool &nonc1test1positive;
ae_int_t &nonc1fidx;
double &nonc1lipschitzc;
ae_bool &badgradsuspected;
ae_int_t &badgradfidx;
ae_int_t &badgradvidx;
real_1d_array badgradxbase;
real_2d_array badgraduser;
real_2d_array badgradnum;
};
/*************************************************************************
This structure is used for detailed reporting about suspected C0
continuity violation.
=== WHAT IS TESTED =======================================================
C0 test studies function values (not gradient!) obtained during line
searches and monitors estimate of the Lipschitz constant. Sudden spikes
usually indicate that discontinuity was detected.
=== WHAT IS REPORTED =====================================================
Actually, report retrieval function returns TWO report structures:
* one for most suspicious point found so far (one with highest change in
the function value), so called "strongest" report
* another one for most detailed line search (more function evaluations =
easier to understand what's going on) which triggered test #0 criteria,
so called "longest" report
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* fidx - is an index of the function (0 for target function, 1 or higher
for nonlinear constraints) which is suspected of being "non-C1"
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
You can plot function values stored in stp[] and f[] arrays and study
behavior of your function by your own eyes, just to be sure that test
correctly reported C1 violation.
-- ALGLIB --
Copyright 19.11.2018 by Bochkanov Sergey
*************************************************************************/
class _optguardnonc0report_owner
{
public:
_optguardnonc0report_owner();
_optguardnonc0report_owner(const _optguardnonc0report_owner &rhs);
_optguardnonc0report_owner& operator=(const _optguardnonc0report_owner &rhs);
virtual ~_optguardnonc0report_owner();
alglib_impl::optguardnonc0report* c_ptr();
alglib_impl::optguardnonc0report* c_ptr() const;
protected:
alglib_impl::optguardnonc0report *p_struct;
};
class optguardnonc0report : public _optguardnonc0report_owner
{
public:
optguardnonc0report();
optguardnonc0report(const optguardnonc0report &rhs);
optguardnonc0report& operator=(const optguardnonc0report &rhs);
virtual ~optguardnonc0report();
ae_bool &positive;
ae_int_t &fidx;
real_1d_array x0;
real_1d_array d;
ae_int_t &n;
real_1d_array stp;
real_1d_array f;
ae_int_t &cnt;
ae_int_t &stpidxa;
ae_int_t &stpidxb;
};
/*************************************************************************
This structure is used for detailed reporting about suspected C1
continuity violation as flagged by C1 test #0 (OptGuard has several tests
for C1 continuity, this report is used by #0).
=== WHAT IS TESTED =======================================================
C1 test #0 studies function values (not gradient!) obtained during line
searches and monitors behavior of directional derivative estimate. This
test is less powerful than test #1, but it does not depend on gradient
values and thus it is more robust against artifacts introduced by
numerical differentiation.
=== WHAT IS REPORTED =====================================================
Actually, report retrieval function returns TWO report structures:
* one for most suspicious point found so far (one with highest change in
the directional derivative), so called "strongest" report
* another one for most detailed line search (more function evaluations =
easier to understand what's going on) which triggered test #0 criteria,
so called "longest" report
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* fidx - is an index of the function (0 for target function, 1 or higher
for nonlinear constraints) which is suspected of being "non-C1"
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
You can plot function values stored in stp[] and f[] arrays and study
behavior of your function by your own eyes, just to be sure that test
correctly reported C1 violation.
-- ALGLIB --
Copyright 19.11.2018 by Bochkanov Sergey
*************************************************************************/
class _optguardnonc1test0report_owner
{
public:
_optguardnonc1test0report_owner();
_optguardnonc1test0report_owner(const _optguardnonc1test0report_owner &rhs);
_optguardnonc1test0report_owner& operator=(const _optguardnonc1test0report_owner &rhs);
virtual ~_optguardnonc1test0report_owner();
alglib_impl::optguardnonc1test0report* c_ptr();
alglib_impl::optguardnonc1test0report* c_ptr() const;
protected:
alglib_impl::optguardnonc1test0report *p_struct;
};
class optguardnonc1test0report : public _optguardnonc1test0report_owner
{
public:
optguardnonc1test0report();
optguardnonc1test0report(const optguardnonc1test0report &rhs);
optguardnonc1test0report& operator=(const optguardnonc1test0report &rhs);
virtual ~optguardnonc1test0report();
ae_bool &positive;
ae_int_t &fidx;
real_1d_array x0;
real_1d_array d;
ae_int_t &n;
real_1d_array stp;
real_1d_array f;
ae_int_t &cnt;
ae_int_t &stpidxa;
ae_int_t &stpidxb;
};
/*************************************************************************
This structure is used for detailed reporting about suspected C1
continuity violation as flagged by C1 test #1 (OptGuard has several tests
for C1 continuity, this report is used by #1).
=== WHAT IS TESTED =======================================================
C1 test #1 studies individual components of the gradient as recorded
during line searches. Upon discovering discontinuity in the gradient this
test records specific component which was suspected (or one with highest
indication of discontinuity if multiple components are suspected).
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
=== WHAT IS REPORTED =====================================================
Actually, report retrieval function returns TWO report structures:
* one for most suspicious point found so far (one with highest change in
the directional derivative), so called "strongest" report
* another one for most detailed line search (more function evaluations =
easier to understand what's going on) which triggered test #1 criteria,
so called "longest" report
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* fidx - is an index of the function (0 for target function, 1 or higher
for nonlinear constraints) which is suspected of being "non-C1"
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
You can plot function values stored in stp[] and g[] arrays and study
behavior of your function by your own eyes, just to be sure that test
correctly reported C1 violation.
-- ALGLIB --
Copyright 19.11.2018 by Bochkanov Sergey
*************************************************************************/
class _optguardnonc1test1report_owner
{
public:
_optguardnonc1test1report_owner();
_optguardnonc1test1report_owner(const _optguardnonc1test1report_owner &rhs);
_optguardnonc1test1report_owner& operator=(const _optguardnonc1test1report_owner &rhs);
virtual ~_optguardnonc1test1report_owner();
alglib_impl::optguardnonc1test1report* c_ptr();
alglib_impl::optguardnonc1test1report* c_ptr() const;
protected:
alglib_impl::optguardnonc1test1report *p_struct;
};
class optguardnonc1test1report : public _optguardnonc1test1report_owner
{
public:
optguardnonc1test1report();
optguardnonc1test1report(const optguardnonc1test1report &rhs);
optguardnonc1test1report& operator=(const optguardnonc1test1report &rhs);
virtual ~optguardnonc1test1report();
ae_bool &positive;
ae_int_t &fidx;
ae_int_t &vidx;
real_1d_array x0;
real_1d_array d;
ae_int_t &n;
real_1d_array stp;
real_1d_array g;
ae_int_t &cnt;
ae_int_t &stpidxa;
ae_int_t &stpidxb;
};
#endif
#if defined(AE_COMPILE_OPTSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SNNLS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SACTIVESETS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_QQPSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_LPQPSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_VIPMSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_NLCSQP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINLBFGS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
*************************************************************************/
class _minlbfgsstate_owner
{
public:
_minlbfgsstate_owner();
_minlbfgsstate_owner(const _minlbfgsstate_owner &rhs);
_minlbfgsstate_owner& operator=(const _minlbfgsstate_owner &rhs);
virtual ~_minlbfgsstate_owner();
alglib_impl::minlbfgsstate* c_ptr();
alglib_impl::minlbfgsstate* c_ptr() const;
protected:
alglib_impl::minlbfgsstate *p_struct;
};
class minlbfgsstate : public _minlbfgsstate_owner
{
public:
minlbfgsstate();
minlbfgsstate(const minlbfgsstate &rhs);
minlbfgsstate& operator=(const minlbfgsstate &rhs);
virtual ~minlbfgsstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called minlbfgsrequesttermination().
X contains point which was "current accepted" when termination
request was submitted.
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minlbfgsreport_owner
{
public:
_minlbfgsreport_owner();
_minlbfgsreport_owner(const _minlbfgsreport_owner &rhs);
_minlbfgsreport_owner& operator=(const _minlbfgsreport_owner &rhs);
virtual ~_minlbfgsreport_owner();
alglib_impl::minlbfgsreport* c_ptr();
alglib_impl::minlbfgsreport* c_ptr() const;
protected:
alglib_impl::minlbfgsreport *p_struct;
};
class minlbfgsreport : public _minlbfgsreport_owner
{
public:
minlbfgsreport();
minlbfgsreport(const minlbfgsreport &rhs);
minlbfgsreport& operator=(const minlbfgsreport &rhs);
virtual ~minlbfgsreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &terminationtype;
};
#endif
#if defined(AE_COMPILE_QPDENSEAULSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINBLEIC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinBLEIC subpackage to work with this
object
*************************************************************************/
class _minbleicstate_owner
{
public:
_minbleicstate_owner();
_minbleicstate_owner(const _minbleicstate_owner &rhs);
_minbleicstate_owner& operator=(const _minbleicstate_owner &rhs);
virtual ~_minbleicstate_owner();
alglib_impl::minbleicstate* c_ptr();
alglib_impl::minbleicstate* c_ptr() const;
protected:
alglib_impl::minbleicstate *p_struct;
};
class minbleicstate : public _minbleicstate_owner
{
public:
minbleicstate();
minbleicstate(const minbleicstate &rhs);
minbleicstate& operator=(const minbleicstate &rhs);
virtual ~minbleicstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount number of iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-3 inconsistent constraints. Feasible point is
either nonexistent or too hard to find. Try to
restart optimizer with better initial approximation
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called minbleicrequesttermination(). X contains
point which was "current accepted" when termination request was
submitted.
ADDITIONAL FIELDS
There are additional fields which can be used for debugging:
* DebugEqErr error in the equality constraints (2-norm)
* DebugFS f, calculated at projection of initial point
to the feasible set
* DebugFF f, calculated at the final point
* DebugDX |X_start-X_final|
*************************************************************************/
class _minbleicreport_owner
{
public:
_minbleicreport_owner();
_minbleicreport_owner(const _minbleicreport_owner &rhs);
_minbleicreport_owner& operator=(const _minbleicreport_owner &rhs);
virtual ~_minbleicreport_owner();
alglib_impl::minbleicreport* c_ptr();
alglib_impl::minbleicreport* c_ptr() const;
protected:
alglib_impl::minbleicreport *p_struct;
};
class minbleicreport : public _minbleicreport_owner
{
public:
minbleicreport();
minbleicreport(const minbleicreport &rhs);
minbleicreport& operator=(const minbleicreport &rhs);
virtual ~minbleicreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &terminationtype;
double &debugeqerr;
double &debugfs;
double &debugff;
double &debugdx;
ae_int_t &debugfeasqpits;
ae_int_t &debugfeasgpaits;
ae_int_t &inneriterationscount;
ae_int_t &outeriterationscount;
};
#endif
#if defined(AE_COMPILE_QPBLEICSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINQP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinQP subpackage to work with this
object
*************************************************************************/
class _minqpstate_owner
{
public:
_minqpstate_owner();
_minqpstate_owner(const _minqpstate_owner &rhs);
_minqpstate_owner& operator=(const _minqpstate_owner &rhs);
virtual ~_minqpstate_owner();
alglib_impl::minqpstate* c_ptr();
alglib_impl::minqpstate* c_ptr() const;
protected:
alglib_impl::minqpstate *p_struct;
};
class minqpstate : public _minqpstate_owner
{
public:
minqpstate();
minqpstate(const minqpstate &rhs);
minqpstate& operator=(const minqpstate &rhs);
virtual ~minqpstate();
};
/*************************************************************************
This structure stores optimization report:
* InnerIterationsCount number of inner iterations
* OuterIterationsCount number of outer iterations
* NCholesky number of Cholesky decomposition
* NMV number of matrix-vector products
(only products calculated as part of iterative
process are counted)
* TerminationType completion code (see below)
* LagBC Lagrange multipliers for box constraints,
array[N], not filled by QP-BLEIC solver
* LagLC Lagrange multipliers for linear constraints,
array[MSparse+MDense], ignored by QP-BLEIC solver
=== COMPLETION CODES =====================================================
Completion codes:
* -9 failure of the automatic scale evaluation: one of the diagonal
elements of the quadratic term is non-positive. Specify variable
scales manually!
* -5 inappropriate solver was used:
* QuickQP solver for problem with general linear constraints (dense/sparse)
* -4 BLEIC-QP or QuickQP solver found unconstrained direction
of negative curvature (function is unbounded from
below even under constraints), no meaningful
minimum can be found.
* -3 inconsistent constraints (or, maybe, feasible point is
too hard to find). If you are sure that constraints are feasible,
try to restart optimizer with better initial approximation.
* -1 solver error
* 1..4 successful completion
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
=== LAGRANGE MULTIPLIERS =================================================
Some optimizers report values of Lagrange multipliers on successful
completion (positive completion code):
* DENSE-IPM-QP and SPARSE-IPM-QP return very precise Lagrange multipliers
as determined during solution process.
* DENSE-AUL-QP returns approximate Lagrange multipliers (which are very
close to "true" Lagrange multipliers except for overconstrained or
degenerate problems)
Two arrays of multipliers are returned:
* LagBC is array[N] which is loaded with multipliers from box constraints;
LagBC[i]>0 means that I-th constraint is at the upper bound, LagBC[I]<0
means that I-th constraint is at the lower bound, LagBC[I]=0 means that
I-th box constraint is inactive.
* LagLC is array[MSparse+MDense] which is loaded with multipliers from
general linear constraints (former MSparse elements corresponds to
sparse part of the constraint matrix, latter MDense are for the dense
constraints, as was specified by user).
LagLC[i]>0 means that I-th constraint at the upper bound, LagLC[i]<0
means that I-th constraint is at the lower bound, LagLC[i]=0 means that
I-th linear constraint is inactive.
On failure (or when optimizer does not support Lagrange multipliers) these
arrays are zero-filled.
NOTE: methods from IPM family may also return meaningful Lagrange
multipliers on completion with codes -3 (infeasibility detected) and
-4 (unboundedness detected). It is possible that seeming
infeasibility/unboundedness of the problem is due to rounding errors
In this case last values of Lagrange multipliers are returned.
*************************************************************************/
class _minqpreport_owner
{
public:
_minqpreport_owner();
_minqpreport_owner(const _minqpreport_owner &rhs);
_minqpreport_owner& operator=(const _minqpreport_owner &rhs);
virtual ~_minqpreport_owner();
alglib_impl::minqpreport* c_ptr();
alglib_impl::minqpreport* c_ptr() const;
protected:
alglib_impl::minqpreport *p_struct;
};
class minqpreport : public _minqpreport_owner
{
public:
minqpreport();
minqpreport(const minqpreport &rhs);
minqpreport& operator=(const minqpreport &rhs);
virtual ~minqpreport();
ae_int_t &inneriterationscount;
ae_int_t &outeriterationscount;
ae_int_t &nmv;
ae_int_t &ncholesky;
ae_int_t &terminationtype;
real_1d_array lagbc;
real_1d_array laglc;
};
#endif
#if defined(AE_COMPILE_REVISEDDUALSIMPLEX) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINLP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores linear solver state.
You should use functions provided by MinLP subpackage to work with this
object
*************************************************************************/
class _minlpstate_owner
{
public:
_minlpstate_owner();
_minlpstate_owner(const _minlpstate_owner &rhs);
_minlpstate_owner& operator=(const _minlpstate_owner &rhs);
virtual ~_minlpstate_owner();
alglib_impl::minlpstate* c_ptr();
alglib_impl::minlpstate* c_ptr() const;
protected:
alglib_impl::minlpstate *p_struct;
};
class minlpstate : public _minlpstate_owner
{
public:
minlpstate();
minlpstate(const minlpstate &rhs);
minlpstate& operator=(const minlpstate &rhs);
virtual ~minlpstate();
};
/*************************************************************************
This structure stores optimization report:
* f target function value
* y dual variables
* stats array[N+M], statuses of box (N) and linear (M)
constraints:
* stats[i]>0 => constraint at upper bound
(also used for free non-basic
variables set to zero)
* stats[i]<0 => constraint at lower bound
* stats[i]=0 => constraint is inactive, basic
variable
* primalerror primal feasibility error
* dualerror dual feasibility error
* iterationscount iteration count
* terminationtype completion code (see below)
Completion codes:
* -4 LP problem is primal unbounded (dual infeasible)
* -3 LP problem is primal infeasible (dual unbounded)
* 1..4 successful completion
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
*************************************************************************/
class _minlpreport_owner
{
public:
_minlpreport_owner();
_minlpreport_owner(const _minlpreport_owner &rhs);
_minlpreport_owner& operator=(const _minlpreport_owner &rhs);
virtual ~_minlpreport_owner();
alglib_impl::minlpreport* c_ptr();
alglib_impl::minlpreport* c_ptr() const;
protected:
alglib_impl::minlpreport *p_struct;
};
class minlpreport : public _minlpreport_owner
{
public:
minlpreport();
minlpreport(const minlpreport &rhs);
minlpreport& operator=(const minlpreport &rhs);
virtual ~minlpreport();
double &f;
real_1d_array y;
integer_1d_array stats;
double &primalerror;
double &dualerror;
ae_int_t &iterationscount;
ae_int_t &terminationtype;
};
#endif
#if defined(AE_COMPILE_NLCSLP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINNLC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinNLC subpackage to work with this
object
*************************************************************************/
class _minnlcstate_owner
{
public:
_minnlcstate_owner();
_minnlcstate_owner(const _minnlcstate_owner &rhs);
_minnlcstate_owner& operator=(const _minnlcstate_owner &rhs);
virtual ~_minnlcstate_owner();
alglib_impl::minnlcstate* c_ptr();
alglib_impl::minnlcstate* c_ptr() const;
protected:
alglib_impl::minnlcstate *p_struct;
};
class minnlcstate : public _minnlcstate_owner
{
public:
minnlcstate();
minnlcstate(const minnlcstate &rhs);
minnlcstate& operator=(const minnlcstate &rhs);
virtual ~minnlcstate();
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
These fields store optimization report:
* iterationscount total number of inner iterations
* nfev number of gradient evaluations
* terminationtype termination type (see below)
Scaled constraint violations are reported:
* bcerr maximum violation of the box constraints
* bcidx index of the most violated box constraint (or
-1, if all box constraints are satisfied or
there is no box constraint)
* lcerr maximum violation of the linear constraints,
computed as maximum scaled distance between
final point and constraint boundary.
* lcidx index of the most violated linear constraint
(or -1, if all constraints are satisfied or
there is no general linear constraints)
* nlcerr maximum violation of the nonlinear constraints
* nlcidx index of the most violated nonlinear constraint
(or -1, if all constraints are satisfied or
there is no nonlinear constraints)
Violations of box constraints are scaled on per-component basis according
to the scale vector s[] as specified by minnlcsetscale(). Violations of
the general linear constraints are also computed using user-supplied
variable scaling. Violations of nonlinear constraints are computed "as is"
TERMINATION CODES
TerminationType field contains completion code, which can be either:
=== FAILURE CODE ===
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signaled.
-3 box constraints are infeasible. Note: infeasibility of non-box
constraints does NOT trigger emergency completion; you have to
examine bcerr/lcerr/nlcerr to detect possibly inconsistent
constraints.
=== SUCCESS CODE ===
2 relative step is no more than EpsX.
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 user requested algorithm termination via minnlcrequesttermination(),
last accepted point is returned
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minnlcreport_owner
{
public:
_minnlcreport_owner();
_minnlcreport_owner(const _minnlcreport_owner &rhs);
_minnlcreport_owner& operator=(const _minnlcreport_owner &rhs);
virtual ~_minnlcreport_owner();
alglib_impl::minnlcreport* c_ptr();
alglib_impl::minnlcreport* c_ptr() const;
protected:
alglib_impl::minnlcreport *p_struct;
};
class minnlcreport : public _minnlcreport_owner
{
public:
minnlcreport();
minnlcreport(const minnlcreport &rhs);
minnlcreport& operator=(const minnlcreport &rhs);
virtual ~minnlcreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &terminationtype;
double &bcerr;
ae_int_t &bcidx;
double &lcerr;
ae_int_t &lcidx;
double &nlcerr;
ae_int_t &nlcidx;
ae_int_t &dbgphase0its;
};
#endif
#if defined(AE_COMPILE_MINBC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinBC subpackage to work with this
object
*************************************************************************/
class _minbcstate_owner
{
public:
_minbcstate_owner();
_minbcstate_owner(const _minbcstate_owner &rhs);
_minbcstate_owner& operator=(const _minbcstate_owner &rhs);
virtual ~_minbcstate_owner();
alglib_impl::minbcstate* c_ptr();
alglib_impl::minbcstate* c_ptr() const;
protected:
alglib_impl::minbcstate *p_struct;
};
class minbcstate : public _minbcstate_owner
{
public:
minbcstate();
minbcstate(const minbcstate &rhs);
minbcstate& operator=(const minbcstate &rhs);
virtual ~minbcstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* iterationscount number of iterations
* nfev number of gradient evaluations
* terminationtype termination type (see below)
TERMINATION CODES
terminationtype field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-3 inconsistent constraints.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called minbcrequesttermination(). X contains
point which was "current accepted" when termination request was
submitted.
*************************************************************************/
class _minbcreport_owner
{
public:
_minbcreport_owner();
_minbcreport_owner(const _minbcreport_owner &rhs);
_minbcreport_owner& operator=(const _minbcreport_owner &rhs);
virtual ~_minbcreport_owner();
alglib_impl::minbcreport* c_ptr();
alglib_impl::minbcreport* c_ptr() const;
protected:
alglib_impl::minbcreport *p_struct;
};
class minbcreport : public _minbcreport_owner
{
public:
minbcreport();
minbcreport(const minbcreport &rhs);
minbcreport& operator=(const minbcreport &rhs);
virtual ~minbcreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &varidx;
ae_int_t &terminationtype;
};
#endif
#if defined(AE_COMPILE_MINNS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores nonlinear optimizer state.
You should use functions provided by MinNS subpackage to work with this
object
*************************************************************************/
class _minnsstate_owner
{
public:
_minnsstate_owner();
_minnsstate_owner(const _minnsstate_owner &rhs);
_minnsstate_owner& operator=(const _minnsstate_owner &rhs);
virtual ~_minnsstate_owner();
alglib_impl::minnsstate* c_ptr();
alglib_impl::minnsstate* c_ptr() const;
protected:
alglib_impl::minnsstate *p_struct;
};
class minnsstate : public _minnsstate_owner
{
public:
minnsstate();
minnsstate(const minnsstate &rhs);
minnsstate& operator=(const minnsstate &rhs);
virtual ~minnsstate();
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
* CErr maximum violation of all types of constraints
* LCErr maximum violation of linear constraints
* NLCErr maximum violation of nonlinear constraints
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
-3 box constraints are inconsistent
-1 inconsistent parameters were passed:
* penalty parameter for minnssetalgoags() is zero,
but we have nonlinear constraints set by minnssetnlc()
2 sampling radius decreased below epsx
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 User requested termination via MinNSRequestTermination()
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _minnsreport_owner
{
public:
_minnsreport_owner();
_minnsreport_owner(const _minnsreport_owner &rhs);
_minnsreport_owner& operator=(const _minnsreport_owner &rhs);
virtual ~_minnsreport_owner();
alglib_impl::minnsreport* c_ptr();
alglib_impl::minnsreport* c_ptr() const;
protected:
alglib_impl::minnsreport *p_struct;
};
class minnsreport : public _minnsreport_owner
{
public:
minnsreport();
minnsreport(const minnsreport &rhs);
minnsreport& operator=(const minnsreport &rhs);
virtual ~minnsreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
double &cerr;
double &lcerr;
double &nlcerr;
ae_int_t &terminationtype;
ae_int_t &varidx;
ae_int_t &funcidx;
};
#endif
#if defined(AE_COMPILE_MINCOMP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
*************************************************************************/
class _minasastate_owner
{
public:
_minasastate_owner();
_minasastate_owner(const _minasastate_owner &rhs);
_minasastate_owner& operator=(const _minasastate_owner &rhs);
virtual ~_minasastate_owner();
alglib_impl::minasastate* c_ptr();
alglib_impl::minasastate* c_ptr() const;
protected:
alglib_impl::minasastate *p_struct;
};
class minasastate : public _minasastate_owner
{
public:
minasastate();
minasastate(const minasastate &rhs);
minasastate& operator=(const minasastate &rhs);
virtual ~minasastate();
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
*************************************************************************/
class _minasareport_owner
{
public:
_minasareport_owner();
_minasareport_owner(const _minasareport_owner &rhs);
_minasareport_owner& operator=(const _minasareport_owner &rhs);
virtual ~_minasareport_owner();
alglib_impl::minasareport* c_ptr();
alglib_impl::minasareport* c_ptr() const;
protected:
alglib_impl::minasareport *p_struct;
};
class minasareport : public _minasareport_owner
{
public:
minasareport();
minasareport(const minasareport &rhs);
minasareport& operator=(const minasareport &rhs);
virtual ~minasareport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &terminationtype;
ae_int_t &activeconstraints;
};
#endif
#if defined(AE_COMPILE_MINCG) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This object stores state of the nonlinear CG optimizer.
You should use ALGLIB functions to work with this object.
*************************************************************************/
class _mincgstate_owner
{
public:
_mincgstate_owner();
_mincgstate_owner(const _mincgstate_owner &rhs);
_mincgstate_owner& operator=(const _mincgstate_owner &rhs);
virtual ~_mincgstate_owner();
alglib_impl::mincgstate* c_ptr();
alglib_impl::mincgstate* c_ptr() const;
protected:
alglib_impl::mincgstate *p_struct;
};
class mincgstate : public _mincgstate_owner
{
public:
mincgstate();
mincgstate(const mincgstate &rhs);
mincgstate& operator=(const mincgstate &rhs);
virtual ~mincgstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &xupdated;
double &f;
real_1d_array g;
real_1d_array x;
};
/*************************************************************************
This structure stores optimization report:
* IterationsCount total number of inner iterations
* NFEV number of gradient evaluations
* TerminationType termination type (see below)
TERMINATION CODES
TerminationType field contains completion code, which can be:
-8 internal integrity control detected infinite or NAN values in
function/gradient. Abnormal termination signalled.
1 relative function improvement is no more than EpsF.
2 relative step is no more than EpsX.
4 gradient norm is no more than EpsG
5 MaxIts steps was taken
7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
8 terminated by user who called mincgrequesttermination(). X contains
point which was "current accepted" when termination request was
submitted.
Other fields of this structure are not documented and should not be used!
*************************************************************************/
class _mincgreport_owner
{
public:
_mincgreport_owner();
_mincgreport_owner(const _mincgreport_owner &rhs);
_mincgreport_owner& operator=(const _mincgreport_owner &rhs);
virtual ~_mincgreport_owner();
alglib_impl::mincgreport* c_ptr();
alglib_impl::mincgreport* c_ptr() const;
protected:
alglib_impl::mincgreport *p_struct;
};
class mincgreport : public _mincgreport_owner
{
public:
mincgreport();
mincgreport(const mincgreport &rhs);
mincgreport& operator=(const mincgreport &rhs);
virtual ~mincgreport();
ae_int_t &iterationscount;
ae_int_t &nfev;
ae_int_t &terminationtype;
};
#endif
#if defined(AE_COMPILE_MINLM) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Levenberg-Marquardt optimizer.
This structure should be created using one of the MinLMCreate???()
functions. You should not access its fields directly; use ALGLIB functions
to work with it.
*************************************************************************/
class _minlmstate_owner
{
public:
_minlmstate_owner();
_minlmstate_owner(const _minlmstate_owner &rhs);
_minlmstate_owner& operator=(const _minlmstate_owner &rhs);
virtual ~_minlmstate_owner();
alglib_impl::minlmstate* c_ptr();
alglib_impl::minlmstate* c_ptr() const;
protected:
alglib_impl::minlmstate *p_struct;
};
class minlmstate : public _minlmstate_owner
{
public:
minlmstate();
minlmstate(const minlmstate &rhs);
minlmstate& operator=(const minlmstate &rhs);
virtual ~minlmstate();
ae_bool &needf;
ae_bool &needfg;
ae_bool &needfgh;
ae_bool &needfi;
ae_bool &needfij;
ae_bool &xupdated;
double &f;
real_1d_array fi;
real_1d_array g;
real_2d_array h;
real_2d_array j;
real_1d_array x;
};
/*************************************************************************
Optimization report, filled by MinLMResults() function
FIELDS:
* TerminationType, completetion code:
* -8 optimizer detected NAN/INF values either in the function itself,
or in its Jacobian
* -5 inappropriate solver was used:
* solver created with minlmcreatefgh() used on problem with
general linear constraints (set with minlmsetlc() call).
* -3 constraints are inconsistent
* 2 relative step is no more than EpsX.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called MinLMRequestTermination().
X contains point which was "current accepted" when termination
request was submitted.
* IterationsCount, contains iterations count
* NFunc, number of function calculations
* NJac, number of Jacobi matrix calculations
* NGrad, number of gradient calculations
* NHess, number of Hessian calculations
* NCholesky, number of Cholesky decomposition calculations
*************************************************************************/
class _minlmreport_owner
{
public:
_minlmreport_owner();
_minlmreport_owner(const _minlmreport_owner &rhs);
_minlmreport_owner& operator=(const _minlmreport_owner &rhs);
virtual ~_minlmreport_owner();
alglib_impl::minlmreport* c_ptr();
alglib_impl::minlmreport* c_ptr() const;
protected:
alglib_impl::minlmreport *p_struct;
};
class minlmreport : public _minlmreport_owner
{
public:
minlmreport();
minlmreport(const minlmreport &rhs);
minlmreport& operator=(const minlmreport &rhs);
virtual ~minlmreport();
ae_int_t &iterationscount;
ae_int_t &terminationtype;
ae_int_t &nfunc;
ae_int_t &njac;
ae_int_t &ngrad;
ae_int_t &nhess;
ae_int_t &ncholesky;
};
#endif
#if defined(AE_COMPILE_CQMODELS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_OPTGUARDAPI) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_OPTSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SNNLS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SACTIVESETS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_QQPSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_LPQPSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_VIPMSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_NLCSQP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINLBFGS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
LIMITED MEMORY BFGS METHOD FOR LARGE SCALE OPTIMIZATION
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments by using a quasi-
Newton method (LBFGS scheme) which is optimized to use a minimum amount
of memory.
The subroutine generates the approximation of an inverse Hessian matrix by
using information about the last M steps of the algorithm (instead of N).
It lessens a required amount of memory from a value of order N^2 to a
value of order 2*N*M.
REQUIREMENTS:
Algorithm will request following information during its operation:
* function value F and its gradient G (simultaneously) at given point X
USAGE:
1. User initializes algorithm state with MinLBFGSCreate() call
2. User tunes solver parameters with MinLBFGSSetCond() MinLBFGSSetStpMax()
and other functions
3. User calls MinLBFGSOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
4. User calls MinLBFGSResults() to get solution
5. Optionally user may call MinLBFGSRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLBFGSRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension. N>0
M - number of corrections in the BFGS scheme of Hessian
approximation update. Recommended value: 3<=M<=7. The smaller
value causes worse convergence, the bigger will not cause a
considerably better convergence, but will cause a fall in the
performance. M<=N.
X - initial solution approximation, array[0..N-1].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLBFGSSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLBFGSSetStpMax() function to bound algorithm's steps. However,
L-BFGS rarely needs such a tuning.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgscreate(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
void minlbfgscreate(const ae_int_t m, const real_1d_array &x, minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
The subroutine is finite difference variant of MinLBFGSCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinLBFGSCreate() in order to get
more information about creation of LBFGS optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of corrections in the BFGS scheme of Hessian
approximation update. Recommended value: 3<=M<=7. The smaller
value causes worse convergence, the bigger will not cause a
considerably better convergence, but will cause a fall in the
performance. M<=N.
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinLBFGSSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. LBFGS needs exact gradient values.
Imprecise gradient may slow down convergence, especially on highly
nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void minlbfgscreatef(const ae_int_t n, const ae_int_t m, const real_1d_array &x, const double diffstep, minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
void minlbfgscreatef(const ae_int_t m, const real_1d_array &x, const double diffstep, minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for L-BFGS optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinLBFGSSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinLBFGSSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetcond(const minlbfgsstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinLBFGSOptimize().
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetxrep(const minlbfgsstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0 (default), if
you don't want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetstpmax(const minlbfgsstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for LBFGS optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the LBFGS too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinLBFGSSetPrec...()
functions.
There is special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetscale(const minlbfgsstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: default preconditioner (simple
scaling, same for all elements of X) is used.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecdefault(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: Cholesky factorization of approximate
Hessian is used.
INPUT PARAMETERS:
State - structure which stores algorithm state
P - triangular preconditioner, Cholesky factorization of
the approximate Hessian. array[0..N-1,0..N-1],
(if larger, only leading N elements are used).
IsUpper - whether upper or lower triangle of P is given
(other triangle is not referenced)
After call to this function preconditioner is changed to P (P is copied
into the internal buffer).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: P should be nonsingular. Exception will be thrown otherwise.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetpreccholesky(const minlbfgsstate &state, const real_2d_array &p, const bool isupper, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: D[i] should be positive. Exception will be thrown otherwise.
NOTE 3: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecdiag(const minlbfgsstate &state, const real_1d_array &d, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinLBFGSSetScale()
call (before or after MinLBFGSSetPrecScale() call). Without knowledge of
the scale of your variables scale-based preconditioner will be just unit
matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetprecscale(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minlbfgsiteration(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinLBFGSCreate() for analytical gradient or MinLBFGSCreateF()
for numerical differentiation) you should choose appropriate variant of
MinLBFGSOptimize() - one which accepts function AND gradient or one
which accepts function ONLY.
Be careful to choose variant of MinLBFGSOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinLBFGSOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinLBFGSOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinLBFGSCreateF() | work FAIL
MinLBFGSCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinLBFGSOptimize() version. Attemps to use such
combination (for example, to create optimizer with MinLBFGSCreateF() and
to pass gradient information to MinCGOptimize()) will lead to exception
being thrown. Either you did not pass gradient when it WAS needed or
you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptimize(minlbfgsstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minlbfgsoptimize(minlbfgsstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic gradient.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function at the initial point
(note: future versions may also perform check at the final point) and
compares numerical gradient with analytic one provided by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both gradients and specific components highlighted as
suspicious by the OptGuard.
The primary OptGuard report can be retrieved with minlbfgsoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with minlbfgssetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptguardgradient(const minlbfgsstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates nonsmoothness monitoring option of
the OptGuard integrity checker. Smoothness monitor silently observes
solution process and tries to detect ill-posed problems, i.e. ones with:
a) discontinuous target function (non-C0)
b) nonsmooth target function (non-C1)
Smoothness monitoring does NOT interrupt optimization even if it suspects
that your problem is nonsmooth. It just sets corresponding flags in the
OptGuard report which can be retrieved after optimization is over.
Smoothness monitoring is a moderate overhead option which often adds less
than 1% to the optimizer running time. Thus, you can use it even for large
scale problems.
NOTE: OptGuard does NOT guarantee that it will always detect C0/C1
continuity violations.
First, minor errors are hard to catch - say, a 0.0001 difference in
the model values at two sides of the gap may be due to discontinuity
of the model - or simply because the model has changed.
Second, C1-violations are especially difficult to detect in a
noninvasive way. The optimizer usually performs very short steps
near the nonsmoothness, and differentiation usually introduces a
lot of numerical noise. It is hard to tell whether some tiny
discontinuity in the slope is due to real nonsmoothness or just due
to numerical noise alone.
Our top priority was to avoid false positives, so in some rare cases
minor errors may went unnoticed (however, in most cases they can be
spotted with restart from different initial point).
INPUT PARAMETERS:
state - algorithm state
level - monitoring level:
* 0 - monitoring is disabled
* 1 - noninvasive low-overhead monitoring; function values
and/or gradients are recorded, but OptGuard does not
try to perform additional evaluations in order to
get more information about suspicious locations.
=== EXPLANATION ==========================================================
One major source of headache during optimization is the possibility of
the coding errors in the target function/constraints (or their gradients).
Such errors most often manifest themselves as discontinuity or
nonsmoothness of the target/constraints.
Another frequent situation is when you try to optimize something involving
lots of min() and max() operations, i.e. nonsmooth target. Although not a
coding error, it is nonsmoothness anyway - and smooth optimizers usually
stop right after encountering nonsmoothness, well before reaching solution.
OptGuard integrity checker helps you to catch such situations: it monitors
function values/gradients being passed to the optimizer and tries to
errors. Upon discovering suspicious pair of points it raises appropriate
flag (and allows you to continue optimization). When optimization is done,
you can study OptGuard result.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptguardsmoothness(const minlbfgsstate &state, const ae_int_t level, const xparams _xparams = alglib::xdefault);
void minlbfgsoptguardsmoothness(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
=== PRIMARY REPORT =======================================================
OptGuard performs several checks which are intended to catch common errors
in the implementation of nonlinear function/gradient:
* incorrect analytic gradient
* discontinuous (non-C0) target functions (constraints)
* nonsmooth (non-C1) target functions (constraints)
Each of these checks is activated with appropriate function:
* minlbfgsoptguardgradient() for gradient verification
* minlbfgsoptguardsmoothness() for C0/C1 checks
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradvidx for specific variable (gradient element) suspected
* rep.badgradxbase, a point where gradient is tested
* rep.badgraduser, user-provided gradient (stored as 2D matrix with
single row in order to make report structure compatible with more
complex optimizers like MinNLC or MinLM)
* rep.badgradnum, reference gradient obtained via numerical
differentiation (stored as 2D matrix with single row in order to make
report structure compatible with more complex optimizers like MinNLC
or MinLM)
* rep.nonc0suspected
* rep.nonc1suspected
=== ADDITIONAL REPORTS/LOGS ==============================================
Several different tests are performed to catch C0/C1 errors, you can find
out specific test signaled error by looking to:
* rep.nonc0test0positive, for non-C0 test #0
* rep.nonc1test0positive, for non-C1 test #0
* rep.nonc1test1positive, for non-C1 test #1
Additional information (including line search logs) can be obtained by
means of:
* minlbfgsoptguardnonc1test0results()
* minlbfgsoptguardnonc1test1results()
which return detailed error reports, specific points where discontinuities
were found, and so on.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - generic OptGuard report; more detailed reports can be
retrieved with other functions.
NOTE: false negatives (nonsmooth problems are not identified as nonsmooth
ones) are possible although unlikely.
The reason is that you need to make several evaluations around
nonsmoothness in order to accumulate enough information about
function curvature. Say, if you start right from the nonsmooth point,
optimizer simply won't get enough data to understand what is going
wrong before it terminates due to abrupt changes in the derivative.
It is also possible that "unlucky" step will move us to the
termination too quickly.
Our current approach is to have less than 0.1% false negatives in
our test examples (measured with multiple restarts from random
points), and to have exactly 0% false positives.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptguardresults(const minlbfgsstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #0
Nonsmoothness (non-C1) test #0 studies function values (not gradient!)
obtained during line searches and monitors behavior of the directional
derivative estimate.
This test is less powerful than test #1, but it does not depend on the
gradient values and thus it is more robust against artifacts introduced by
numerical differentiation.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #0 "strong" report
lngrep - C1 test #0 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptguardnonc1test0results(const minlbfgsstate &state, optguardnonc1test0report &strrep, optguardnonc1test0report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #1
Nonsmoothness (non-C1) test #1 studies individual components of the
gradient computed during line search.
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #1 "strong" report
lngrep - C1 test #1 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minlbfgsoptguardnonc1test1results(const minlbfgsstate &state, optguardnonc1test1report &strrep, optguardnonc1test1report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
L-BFGS algorithm results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -8 internal integrity control detected infinite
or NAN values in function/gradient. Abnormal
termination signalled.
* -2 rounding errors prevent further improvement.
X contains best point found.
* -1 incorrect parameters were specified
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called minlbfgsrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsresults(const minlbfgsstate &state, real_1d_array &x, minlbfgsreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
L-BFGS algorithm results
Buffered implementation of MinLBFGSResults which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 20.08.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsresultsbuf(const minlbfgsstate &state, real_1d_array &x, minlbfgsreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts LBFGS algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used to store algorithm state
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgsrestartfrom(const minlbfgsstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minlbfgsrequesttermination(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_QPDENSEAULSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINBLEIC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
BOUND CONSTRAINED OPTIMIZATION
WITH ADDITIONAL LINEAR EQUALITY AND INEQUALITY CONSTRAINTS
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
REQUIREMENTS:
* user must provide function value and gradient
* starting point X0 must be feasible or
not too far away from the feasible set
* grad(f) must be Lipschitz continuous on a level set:
L = { x : f(x)<=f(x0) }
* function must be defined everywhere on the feasible set F
USAGE:
Constrained optimization if far more complex than the unconstrained one.
Here we give very brief outline of the BLEIC optimizer. We strongly recommend
you to read examples in the ALGLIB Reference Manual and to read ALGLIB User Guide
on optimization, which is available at http://www.alglib.net/optimization/
1. User initializes algorithm state with MinBLEICCreate() call
2. USer adds boundary and/or linear constraints by calling
MinBLEICSetBC() and MinBLEICSetLC() functions.
3. User sets stopping conditions with MinBLEICSetCond().
4. User calls MinBLEICOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
5. User calls MinBLEICResults() to get solution
6. Optionally user may call MinBLEICRestartFrom() to solve another problem
with same N but another starting point.
MinBLEICRestartFrom() allows to reuse already initialized structure.
NOTE: if you have box-only constraints (no general linear constraints),
then MinBC optimizer can be better option. It uses special, faster
constraint activation method, which performs better on problems with
multiple constraints active at the solution.
On small-scale problems performance of MinBC is similar to that of
MinBLEIC, but on large-scale ones (hundreds and thousands of active
constraints) it can be several times faster than MinBLEIC.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleiccreate(const ae_int_t n, const real_1d_array &x, minbleicstate &state, const xparams _xparams = alglib::xdefault);
void minbleiccreate(const real_1d_array &x, minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
The subroutine is finite difference variant of MinBLEICCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinBLEICCreate() in order to get
more information about creation of BLEIC optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinBLEICSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. CG needs exact gradient values. Imprecise
gradient may slow down convergence, especially on highly nonlinear
problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void minbleiccreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minbleicstate &state, const xparams _xparams = alglib::xdefault);
void minbleiccreatef(const real_1d_array &x, const double diffstep, minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets boundary constraints for BLEIC optimizer.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinBLEICRestartFrom().
NOTE: if you have box-only constraints (no general linear constraints),
then MinBC optimizer can be better option. It uses special, faster
constraint activation method, which performs better on problems with
multiple constraints active at the solution.
On small-scale problems performance of MinBC is similar to that of
MinBLEIC, but on large-scale ones (hundreds and thousands of active
constraints) it can be several times faster than MinBLEIC.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: this solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints,
even when numerical differentiation is used (algorithm adjusts nodes
according to boundary constraints)
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbc(const minbleicstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets linear constraints for BLEIC optimizer.
Linear constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinBLEICRestartFrom().
INPUT PARAMETERS:
State - structure previously allocated with MinBLEICCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: linear (non-bound) constraints are satisfied only approximately:
* there always exists some minor violation (about Epsilon in magnitude)
due to rounding errors
* numerical differentiation, if used, may lead to function evaluations
outside of the feasible area, because algorithm does NOT change
numerical differentiation formula according to linear constraints.
If you want constraints to be satisfied exactly, try to reformulate your
problem in such manner that all constraints will become boundary ones
(this kind of constraints is always satisfied exactly, both in the final
solution and in all intermediate points).
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetlc(const minbleicstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minbleicsetlc(const minbleicstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for the optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinBLEICSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinBLEICSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection.
NOTE: when SetCond() called with non-zero MaxIts, BLEIC solver may perform
slightly more than MaxIts iterations. I.e., MaxIts sets non-strict
limit on iterations count.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetcond(const minbleicstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for BLEIC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the BLEIC too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinBLEICSetPrec...()
functions.
There is a special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minbleicsetscale(const minbleicstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: preconditioning is turned off.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecdefault(const minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE 1: D[i] should be positive. Exception will be thrown otherwise.
NOTE 2: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecdiag(const minbleicstate &state, const real_1d_array &d, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinBLEICSetScale()
call (before or after MinBLEICSetPrecScale() call). Without knowledge of
the scale of your variables scale-based preconditioner will be just unit
matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetprecscale(const minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinBLEICOptimize().
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetxrep(const minbleicstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length
IMPORTANT: this feature is hard to combine with preconditioning. You can't
set upper limit on step length, when you solve optimization problem with
linear (non-boundary) constraints AND preconditioner turned on.
When non-boundary constraints are present, you have to either a) use
preconditioner, or b) use upper limit on step length. YOU CAN'T USE BOTH!
In this case algorithm will terminate with appropriate error code.
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which lead to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetstpmax(const minbleicstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minbleiciteration(const minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinBLEICCreate() for analytical gradient or MinBLEICCreateF()
for numerical differentiation) you should choose appropriate variant of
MinBLEICOptimize() - one which accepts function AND gradient or one
which accepts function ONLY.
Be careful to choose variant of MinBLEICOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinBLEICOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinBLEICOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinBLEICCreateF() | work FAIL
MinBLEICCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinBLEICOptimize() version. Attemps to use such
combination (for example, to create optimizer with MinBLEICCreateF()
and to pass gradient information to MinBLEICOptimize()) will lead to
exception being thrown. Either you did not pass gradient when it WAS
needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicoptimize(minbleicstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minbleicoptimize(minbleicstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic gradient.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function at the initial point
(note: future versions may also perform check at the final point) and
compares numerical gradient with analytic one provided by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both gradients and specific components highlighted as
suspicious by the OptGuard.
The primary OptGuard report can be retrieved with minbleicoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with minbleicsetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minbleicoptguardgradient(const minbleicstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates nonsmoothness monitoring option of
the OptGuard integrity checker. Smoothness monitor silently observes
solution process and tries to detect ill-posed problems, i.e. ones with:
a) discontinuous target function (non-C0)
b) nonsmooth target function (non-C1)
Smoothness monitoring does NOT interrupt optimization even if it suspects
that your problem is nonsmooth. It just sets corresponding flags in the
OptGuard report which can be retrieved after optimization is over.
Smoothness monitoring is a moderate overhead option which often adds less
than 1% to the optimizer running time. Thus, you can use it even for large
scale problems.
NOTE: OptGuard does NOT guarantee that it will always detect C0/C1
continuity violations.
First, minor errors are hard to catch - say, a 0.0001 difference in
the model values at two sides of the gap may be due to discontinuity
of the model - or simply because the model has changed.
Second, C1-violations are especially difficult to detect in a
noninvasive way. The optimizer usually performs very short steps
near the nonsmoothness, and differentiation usually introduces a
lot of numerical noise. It is hard to tell whether some tiny
discontinuity in the slope is due to real nonsmoothness or just due
to numerical noise alone.
Our top priority was to avoid false positives, so in some rare cases
minor errors may went unnoticed (however, in most cases they can be
spotted with restart from different initial point).
INPUT PARAMETERS:
state - algorithm state
level - monitoring level:
* 0 - monitoring is disabled
* 1 - noninvasive low-overhead monitoring; function values
and/or gradients are recorded, but OptGuard does not
try to perform additional evaluations in order to
get more information about suspicious locations.
=== EXPLANATION ==========================================================
One major source of headache during optimization is the possibility of
the coding errors in the target function/constraints (or their gradients).
Such errors most often manifest themselves as discontinuity or
nonsmoothness of the target/constraints.
Another frequent situation is when you try to optimize something involving
lots of min() and max() operations, i.e. nonsmooth target. Although not a
coding error, it is nonsmoothness anyway - and smooth optimizers usually
stop right after encountering nonsmoothness, well before reaching solution.
OptGuard integrity checker helps you to catch such situations: it monitors
function values/gradients being passed to the optimizer and tries to
errors. Upon discovering suspicious pair of points it raises appropriate
flag (and allows you to continue optimization). When optimization is done,
you can study OptGuard result.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbleicoptguardsmoothness(const minbleicstate &state, const ae_int_t level, const xparams _xparams = alglib::xdefault);
void minbleicoptguardsmoothness(const minbleicstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
=== PRIMARY REPORT =======================================================
OptGuard performs several checks which are intended to catch common errors
in the implementation of nonlinear function/gradient:
* incorrect analytic gradient
* discontinuous (non-C0) target functions (constraints)
* nonsmooth (non-C1) target functions (constraints)
Each of these checks is activated with appropriate function:
* minbleicoptguardgradient() for gradient verification
* minbleicoptguardsmoothness() for C0/C1 checks
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradvidx for specific variable (gradient element) suspected
* rep.badgradxbase, a point where gradient is tested
* rep.badgraduser, user-provided gradient (stored as 2D matrix with
single row in order to make report structure compatible with more
complex optimizers like MinNLC or MinLM)
* rep.badgradnum, reference gradient obtained via numerical
differentiation (stored as 2D matrix with single row in order to make
report structure compatible with more complex optimizers like MinNLC
or MinLM)
* rep.nonc0suspected
* rep.nonc1suspected
=== ADDITIONAL REPORTS/LOGS ==============================================
Several different tests are performed to catch C0/C1 errors, you can find
out specific test signaled error by looking to:
* rep.nonc0test0positive, for non-C0 test #0
* rep.nonc1test0positive, for non-C1 test #0
* rep.nonc1test1positive, for non-C1 test #1
Additional information (including line search logs) can be obtained by
means of:
* minbleicoptguardnonc1test0results()
* minbleicoptguardnonc1test1results()
which return detailed error reports, specific points where discontinuities
were found, and so on.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - generic OptGuard report; more detailed reports can be
retrieved with other functions.
NOTE: false negatives (nonsmooth problems are not identified as nonsmooth
ones) are possible although unlikely.
The reason is that you need to make several evaluations around
nonsmoothness in order to accumulate enough information about
function curvature. Say, if you start right from the nonsmooth point,
optimizer simply won't get enough data to understand what is going
wrong before it terminates due to abrupt changes in the derivative.
It is also possible that "unlucky" step will move us to the
termination too quickly.
Our current approach is to have less than 0.1% false negatives in
our test examples (measured with multiple restarts from random
points), and to have exactly 0% false positives.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbleicoptguardresults(const minbleicstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #0
Nonsmoothness (non-C1) test #0 studies function values (not gradient!)
obtained during line searches and monitors behavior of the directional
derivative estimate.
This test is less powerful than test #1, but it does not depend on the
gradient values and thus it is more robust against artifacts introduced by
numerical differentiation.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #0 "strong" report
lngrep - C1 test #0 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbleicoptguardnonc1test0results(const minbleicstate &state, optguardnonc1test0report &strrep, optguardnonc1test0report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #1
Nonsmoothness (non-C1) test #1 studies individual components of the
gradient computed during line search.
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #1 "strong" report
lngrep - C1 test #1 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbleicoptguardnonc1test1results(const minbleicstate &state, optguardnonc1test1report &strrep, optguardnonc1test1report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
BLEIC results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -3 inconsistent constraints. Feasible point is
either nonexistent or too hard to find. Try to
restart optimizer with better initial approximation
* 1 relative function improvement is no more than EpsF.
* 2 scaled step is no more than EpsX.
* 4 scaled gradient norm is no more than EpsG.
* 5 MaxIts steps was taken
* 8 terminated by user who called minbleicrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
More information about fields of this structure can be
found in the comments on MinBLEICReport datatype.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicresults(const minbleicstate &state, real_1d_array &x, minbleicreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
BLEIC results
Buffered implementation of MinBLEICResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicresultsbuf(const minbleicstate &state, real_1d_array &x, minbleicreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with MinBLEICCreate call.
X - new starting point.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicrestartfrom(const minbleicstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minbleicrequesttermination(const minbleicstate &state, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_QPBLEICSOLVER) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINQP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
CONSTRAINED QUADRATIC PROGRAMMING
The subroutine creates QP optimizer. After initial creation, it contains
default optimization problem with zero quadratic and linear terms and no
constraints.
In order to actually solve something you should:
* set cost vector with minqpsetlinearterm()
* set variable bounds with minqpsetbc() or minqpsetbcall()
* specify constraint matrix with one of the following functions:
* modern API:
* minqpsetlc2() for sparse two-sided constraints AL <= A*x <= AU
* minqpsetlc2dense() for dense two-sided constraints AL <= A*x <= AU
* minqpsetlc2mixed() for mixed two-sided constraints AL <= A*x <= AU
* minqpaddlc2dense() to add one dense row to dense constraint submatrix
* minqpaddlc2() to add one sparse row to sparse constraint submatrix
* legacy API:
* minqpsetlc() for dense one-sided equality/inequality constraints
* minqpsetlcsparse() for sparse one-sided equality/inequality constraints
* minqpsetlcmixed() for mixed dense/sparse one-sided equality/inequality constraints
* choose appropriate QP solver and set it and its stopping criteria by
means of minqpsetalgo??????() function
* call minqpoptimize() to run the solver and minqpresults() to get the
solution vector and additional information.
Following solvers are recommended for convex and semidefinite problems:
* QuickQP for dense problems with box-only constraints (or no constraints
at all)
* DENSE-IPM-QP for convex or semidefinite problems with medium (up
to several thousands) variable count, dense/sparse quadratic term and
any number (up to many thousands) of dense/sparse general linear
constraints
* SPARSE-IPM-QP for convex or semidefinite problems with large (many
thousands) variable count, sparse quadratic term AND linear constraints.
If your problem happens to be nonconvex, but either (a) is effectively
convexified under constraints, or (b) has unique solution even with
nonconvex target, then you can use:
* QuickQP for dense nonconvex problems with box-only constraints
* DENSE-AUL-QP for dense nonconvex problems which are effectively
convexified under constraints with up to several thousands of variables
and any (small or large) number of general linear constraints
* QP-BLEIC for dense/sparse problems with small (up to several hundreds)
number of general linear constraints and arbitrarily large variable
count.
INPUT PARAMETERS:
N - problem size
OUTPUT PARAMETERS:
State - optimizer with zero quadratic/linear terms
and no constraints
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpcreate(const ae_int_t n, minqpstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets linear term for QP solver.
By default, linear term is zero.
INPUT PARAMETERS:
State - structure which stores algorithm state
B - linear term, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetlinearterm(const minqpstate &state, const real_1d_array &b, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets dense quadratic term for QP solver. By default,
quadratic term is zero.
IMPORTANT:
This solver minimizes following function:
f(x) = 0.5*x'*A*x + b'*x.
Note that quadratic term has 0.5 before it. So if you want to minimize
f(x) = x^2 + x
you should rewrite your problem as follows:
f(x) = 0.5*(2*x^2) + x
and your matrix A will be equal to [[2.0]], not to [[1.0]]
INPUT PARAMETERS:
State - structure which stores algorithm state
A - matrix, array[N,N]
IsUpper - (optional) storage type:
* if True, symmetric matrix A is given by its upper
triangle, and the lower triangle isn't used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn't used
* if not given, both lower and upper triangles must be
filled.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetquadraticterm(const minqpstate &state, const real_2d_array &a, const bool isupper, const xparams _xparams = alglib::xdefault);
void minqpsetquadraticterm(const minqpstate &state, const real_2d_array &a, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets sparse quadratic term for QP solver. By default,
quadratic term is zero. This function overrides previous calls to
minqpsetquadraticterm() or minqpsetquadratictermsparse().
NOTE: dense solvers like DENSE-AUL-QP or DENSE-IPM-QP will convert this
matrix to dense storage anyway.
IMPORTANT:
This solver minimizes following function:
f(x) = 0.5*x'*A*x + b'*x.
Note that quadratic term has 0.5 before it. So if you want to minimize
f(x) = x^2 + x
you should rewrite your problem as follows:
f(x) = 0.5*(2*x^2) + x
and your matrix A will be equal to [[2.0]], not to [[1.0]]
INPUT PARAMETERS:
State - structure which stores algorithm state
A - matrix, array[N,N]
IsUpper - (optional) storage type:
* if True, symmetric matrix A is given by its upper
triangle, and the lower triangle isn't used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn't used
* if not given, both lower and upper triangles must be
filled.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetquadratictermsparse(const minqpstate &state, const sparsematrix &a, const bool isupper, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets starting point for QP solver. It is useful to have good
initial approximation to the solution, because it will increase speed of
convergence and identification of active constraints.
NOTE: interior point solvers ignore initial point provided by user.
INPUT PARAMETERS:
State - structure which stores algorithm state
X - starting point, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetstartingpoint(const minqpstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets origin for QP solver. By default, following QP program
is solved:
min(0.5*x'*A*x+b'*x)
This function allows to solve different problem:
min(0.5*(x-x_origin)'*A*(x-x_origin)+b'*(x-x_origin))
Specification of non-zero origin affects function being minimized, but not
constraints. Box and linear constraints are still calculated without
origin.
INPUT PARAMETERS:
State - structure which stores algorithm state
XOrigin - origin, array[N].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetorigin(const minqpstate &state, const real_1d_array &xorigin, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances) and as
preconditioner.
Scale of the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the
function
If you do not know how to choose scales of your variables, you can:
* read www.alglib.net/optimization/scaling.php article
* use minqpsetscaleautodiag(), which calculates scale using diagonal of
the quadratic term: S is set to 1/sqrt(diag(A)), which works well
sometimes.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetscale(const minqpstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets automatic evaluation of variable scaling.
IMPORTANT: this function works only for matrices with positive diagonal
elements! Zero or negative elements will result in -9 error
code being returned. Specify scale vector manually with
minqpsetscale() in such cases.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances) and as
preconditioner.
The best way to set scaling is to manually specify variable scales.
However, sometimes you just need quick-and-dirty solution - either when
you perform fast prototyping, or when you know your problem well and you
are 100% sure that this quick solution is robust enough in your case.
One such solution is to evaluate scale of I-th variable as 1/Sqrt(A[i,i]),
where A[i,i] is an I-th diagonal element of the quadratic term.
Such approach works well sometimes, but you have to be careful here.
INPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 26.12.2017 by Bochkanov Sergey
*************************************************************************/
void minqpsetscaleautodiag(const minqpstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells solver to use BLEIC-based algorithm and sets stopping
criteria for the algorithm.
This algorithm is intended for large-scale problems, possibly nonconvex,
with small number of general linear constraints. Feasible initial point is
essential for good performance.
IMPORTANT: when DENSE-IPM (or DENSE-AUL for nonconvex problems) solvers
are applicable, their performance is much better than that of
BLEIC-QP.
We recommend you to use BLEIC only when other solvers can not
be used.
ALGORITHM FEATURES:
* supports dense and sparse QP problems
* supports box and general linear equality/inequality constraints
* can solve all types of problems (convex, semidefinite, nonconvex) as
long as they are bounded from below under constraints.
Say, it is possible to solve "min{-x^2} subject to -1<=x<=+1".
Of course, global minimum is found only for positive definite and
semidefinite problems. As for indefinite ones - only local minimum is
found.
ALGORITHM OUTLINE:
* BLEIC-QP solver is just a driver function for MinBLEIC solver; it solves
quadratic programming problem as general linearly constrained
optimization problem, which is solved by means of BLEIC solver (part of
ALGLIB, active set method).
ALGORITHM LIMITATIONS:
* This algorithm is inefficient on problems with hundreds and thousands
of general inequality constraints and infeasible initial point. Initial
feasibility detection stage may take too long on such constraint sets.
Consider using DENSE-IPM or DENSE-AUL instead.
* unlike QuickQP solver, this algorithm does not perform Newton steps and
does not use Level 3 BLAS. Being general-purpose active set method, it
can activate constraints only one-by-one. Thus, its performance is lower
than that of QuickQP.
* its precision is also a bit inferior to that of QuickQP. BLEIC-QP
performs only LBFGS steps (no Newton steps), which are good at detecting
neighborhood of the solution, buy needs many iterations to find solution
with more than 6 digits of precision.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled constrained gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinQPSetScale()
EpsF - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition: |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
EpsX - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinQPSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. NOTE: this algorithm uses LBFGS
iterations, which are relatively cheap, but improve
function value only a bit. So you will need many iterations
to converge - from 0.1*N to 10*N, depending on problem's
condition number.
IT IS VERY IMPORTANT TO CALL MinQPSetScale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS STOPPING CRITERIA ARE SCALE-DEPENDENT!
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection (presently it is small step
length, but it may change in the future versions of ALGLIB).
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgobleic(const minqpstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells QP solver to use DENSE-AUL algorithm and sets stopping
criteria for the algorithm.
This algorithm is intended for non-convex problems with moderate (up
to several thousands) variable count and arbitrary number of constraints
which are either (a) effectively convexified under constraints or (b) have
unique solution even with nonconvex target.
IMPORTANT: when DENSE-IPM solver is applicable, its performance is usually
much better than that of DENSE-AUL.
We recommend you to use DENSE-AUL only when other solvers can
not be used.
ALGORITHM FEATURES:
* supports box and dense/sparse general linear equality/inequality
constraints
* convergence is theoretically proved for positive-definite (convex) QP
problems. Semidefinite and non-convex problems can be solved as long as
they are bounded from below under constraints, although without
theoretical guarantees.
ALGORITHM OUTLINE:
* this algorithm is an augmented Lagrangian method with dense
preconditioner (hence its name).
* it performs several outer iterations in order to refine values of the
Lagrange multipliers. Single outer iteration is a solution of some
unconstrained optimization problem: first it performs dense Cholesky
factorization of the Hessian in order to build preconditioner (adaptive
regularization is applied to enforce positive definiteness), and then
it uses L-BFGS optimizer to solve optimization problem.
* typically you need about 5-10 outer iterations to converge to solution
ALGORITHM LIMITATIONS:
* because dense Cholesky driver is used, this algorithm has O(N^2) memory
requirements and O(OuterIterations*N^3) minimum running time. From the
practical point of view, it limits its applicability by several
thousands of variables.
From the other side, variables count is the most limiting factor,
and dependence on constraint count is much more lower. Assuming that
constraint matrix is sparse, it may handle tens of thousands of general
linear constraints.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0, stopping criteria for inner optimizer.
Inner iterations are stopped when step length (with
variable scaling being applied) is less than EpsX.
See minqpsetscale() for more information on variable
scaling.
Rho - penalty coefficient, Rho>0:
* large enough that algorithm converges with desired
precision.
* not TOO large to prevent ill-conditioning
* recommended values are 100, 1000 or 10000
ItsCnt - number of outer iterations:
* recommended values: 10-15 (although in most cases it
converges within 5 iterations, you may need a few more
to be sure).
* ItsCnt=0 means that small number of outer iterations is
automatically chosen (10 iterations in current version).
* ItsCnt=1 means that AUL algorithm performs just as usual
penalty method.
* ItsCnt>1 means that AUL algorithm performs specified
number of outer iterations
IT IS VERY IMPORTANT TO CALL minqpsetscale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS CONVERGENCE PROPERTIES AND STOPPING CRITERIA ARE SCALE-DEPENDENT!
NOTE: Passing EpsX=0 will lead to automatic step length selection
(specific step length chosen may change in the future versions of
ALGLIB, so it is better to specify step length explicitly).
-- ALGLIB --
Copyright 20.08.2016 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgodenseaul(const minqpstate &state, const double epsx, const double rho, const ae_int_t itscnt, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells QP solver to use DENSE-IPM QP algorithm and sets
stopping criteria for the algorithm.
This algorithm is intended for convex and semidefinite problems with
moderate (up to several thousands) variable count and arbitrary number of
constraints.
IMPORTANT: this algorithm won't work for nonconvex problems, use DENSE-AUL
or BLEIC-QP instead. If you try to run DENSE-IPM on problem
with indefinite matrix (matrix having at least one negative
eigenvalue) then depending on circumstances it may either (a)
stall at some arbitrary point, or (b) throw exception on
failure of Cholesky decomposition.
ALGORITHM FEATURES:
* supports box and dense/sparse general linear equality/inequality
constraints
ALGORITHM OUTLINE:
* this algorithm is an implementation of interior point method as
formulated by R.J.Vanderbei, with minor modifications to the algorithm
(damped Newton directions are extensively used)
* like all interior point methods, this algorithm tends to converge in
roughly same number of iterations (between 15 and 30) independently from
the problem dimensionality
ALGORITHM LIMITATIONS:
* because dense Cholesky driver is used, for N-dimensional problem with
M dense constaints this algorithm has O(N^2+N*M) memory requirements and
O(N^3+N*M^2) running time.
Having sparse constraints with Z nonzeros per row relaxes storage and
running time down to O(N^2+M*Z) and O(N^3+N*Z^2)
From the practical point of view, it limits its applicability by
several thousands of variables.
From the other side, variables count is the most limiting factor,
and dependence on constraint count is much more lower. Assuming that
constraint matrix is sparse, it may handle tens of thousands of general
linear constraints.
INPUT PARAMETERS:
State - structure which stores algorithm state
Eps - >=0, stopping criteria. The algorithm stops when primal
and dual infeasiblities as well as complementarity gap are
less than Eps.
IT IS VERY IMPORTANT TO CALL minqpsetscale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS CONVERGENCE PROPERTIES AND STOPPING CRITERIA ARE SCALE-DEPENDENT!
NOTE: Passing EpsX=0 will lead to automatic selection of small epsilon.
===== TRACING IPM SOLVER =================================================
IPM solver supports advanced tracing capabilities. You can trace algorithm
output by specifying following trace symbols (case-insensitive) by means
of trace_file() call:
* 'IPM' - for basic trace of algorithm steps and decisions. Only
short scalars (function values and deltas) are printed.
N-dimensional quantities like search directions are NOT
printed.
* 'IPM.DETAILED'- for output of points being visited and search directions
This symbol also implicitly defines 'IPM'. You can
control output format by additionally specifying:
* nothing to output in 6-digit exponential format
* 'PREC.E15' to output in 15-digit exponential format
* 'PREC.F6' to output in 6-digit fixed-point format
By default trace is disabled and adds no overhead to the optimization
process. However, specifying any of the symbols adds some formatting and
output-related overhead.
You may specify multiple symbols by separating them with commas:
>
> alglib::trace_file("IPM.DETAILED,PREC.F6", "path/to/trace.log")
>
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgodenseipm(const minqpstate &state, const double eps, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells QP solver to use SPARSE-IPM QP algorithm and sets
stopping criteria for the algorithm.
This algorithm is intended for convex and semidefinite problems with
large variable and constraint count and sparse quadratic term and
constraints. It is possible to have some limited set of dense linear
constraints - they will be handled separately by dense BLAS - but the more
dense constraints you have, the more time solver needs.
IMPORTANT: internally this solver performs large and sparse (N+M)x(N+M)
triangular factorization. So it expects both quadratic term and
constraints to be highly sparse. However, its running time is
influenced by BOTH fill factor and sparsity pattern.
Generally we expect that no more than few nonzero elements per
row are present. However different sparsity patterns may result
in completely different running times even given same fill
factor.
In many cases this algorithm outperforms DENSE-IPM by order of
magnitude. However, in some cases you may get better results
with DENSE-IPM even when solving sparse task.
IMPORTANT: this algorithm won't work for nonconvex problems, use DENSE-AUL
or BLEIC-QP instead. If you try to run DENSE-IPM on problem
with indefinite matrix (matrix having at least one negative
eigenvalue) then depending on circumstances it may either (a)
stall at some arbitrary point, or (b) throw exception on
failure of Cholesky decomposition.
ALGORITHM FEATURES:
* supports box and dense/sparse general linear equality/inequality
constraints
* specializes on large-scale sparse problems
ALGORITHM OUTLINE:
* this algorithm is an implementation of interior point method as
formulated by R.J.Vanderbei, with minor modifications to the algorithm
(damped Newton directions are extensively used)
* like all interior point methods, this algorithm tends to converge in
roughly same number of iterations (between 15 and 30) independently from
the problem dimensionality
ALGORITHM LIMITATIONS:
* this algorithm may handle moderate number of dense constraints, usually
no more than a thousand of dense ones without losing its efficiency.
INPUT PARAMETERS:
State - structure which stores algorithm state
Eps - >=0, stopping criteria. The algorithm stops when primal
and dual infeasiblities as well as complementarity gap are
less than Eps.
IT IS VERY IMPORTANT TO CALL minqpsetscale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS CONVERGENCE PROPERTIES AND STOPPING CRITERIA ARE SCALE-DEPENDENT!
NOTE: Passing EpsX=0 will lead to automatic selection of small epsilon.
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgosparseipm(const minqpstate &state, const double eps, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells solver to use QuickQP algorithm: special extra-fast
algorithm for problems with box-only constrants. It may solve non-convex
problems as long as they are bounded from below under constraints.
ALGORITHM FEATURES:
* several times faster than DENSE-IPM when running on box-only problem
* utilizes accelerated methods for activation of constraints.
* supports dense and sparse QP problems
* supports ONLY box constraints; general linear constraints are NOT
supported by this solver
* can solve all types of problems (convex, semidefinite, nonconvex) as
long as they are bounded from below under constraints.
Say, it is possible to solve "min{-x^2} subject to -1<=x<=+1".
In convex/semidefinite case global minimum is returned, in nonconvex
case - algorithm returns one of the local minimums.
ALGORITHM OUTLINE:
* algorithm performs two kinds of iterations: constrained CG iterations
and constrained Newton iterations
* initially it performs small number of constrained CG iterations, which
can efficiently activate/deactivate multiple constraints
* after CG phase algorithm tries to calculate Cholesky decomposition and
to perform several constrained Newton steps. If Cholesky decomposition
failed (matrix is indefinite even under constraints), we perform more
CG iterations until we converge to such set of constraints that system
matrix becomes positive definite. Constrained Newton steps greatly
increase convergence speed and precision.
* algorithm interleaves CG and Newton iterations which allows to handle
indefinite matrices (CG phase) and quickly converge after final set of
constraints is found (Newton phase). Combination of CG and Newton phases
is called "outer iteration".
* it is possible to turn off Newton phase (beneficial for semidefinite
problems - Cholesky decomposition will fail too often)
ALGORITHM LIMITATIONS:
* algorithm does not support general linear constraints; only box ones
are supported
* Cholesky decomposition for sparse problems is performed with Skyline
Cholesky solver, which is intended for low-profile matrices. No profile-
reducing reordering of variables is performed in this version of ALGLIB.
* problems with near-zero negative eigenvalues (or exacty zero ones) may
experience about 2-3x performance penalty. The reason is that Cholesky
decomposition can not be performed until we identify directions of zero
and negative curvature and activate corresponding boundary constraints -
but we need a lot of trial and errors because these directions are hard
to notice in the matrix spectrum.
In this case you may turn off Newton phase of algorithm.
Large negative eigenvalues are not an issue, so highly non-convex
problems can be solved very efficiently.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled constrained gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinQPSetScale()
EpsF - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition: |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
EpsX - >=0
The subroutine finishes its work if exploratory steepest
descent step on k+1-th iteration satisfies following
condition:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinQPSetScale()
MaxOuterIts-maximum number of OUTER iterations. One outer iteration
includes some amount of CG iterations (from 5 to ~N) and
one or several (usually small amount) Newton steps. Thus,
one outer iteration has high cost, but can greatly reduce
funcation value.
Use 0 if you do not want to limit number of outer iterations.
UseNewton- use Newton phase or not:
* Newton phase improves performance of positive definite
dense problems (about 2 times improvement can be observed)
* can result in some performance penalty on semidefinite
or slightly negative definite problems - each Newton
phase will bring no improvement (Cholesky failure), but
still will require computational time.
* if you doubt, you can turn off this phase - optimizer
will retain its most of its high speed.
IT IS VERY IMPORTANT TO CALL MinQPSetScale() WHEN YOU USE THIS ALGORITHM
BECAUSE ITS STOPPING CRITERIA ARE SCALE-DEPENDENT!
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection (presently it is small step
length, but it may change in the future versions of ALGLIB).
-- ALGLIB --
Copyright 22.05.2014 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgoquickqp(const minqpstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxouterits, const bool usenewton, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for QP solver
Box constraints are inactive by default (after initial creation). After
being set, they are preserved until explicitly overwritten with another
minqpsetbc() or minqpsetbcall() call, or partially overwritten with
minqpsetbci() call.
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd[i] BndL[i]=BndU[i]
lower bound BndL[i]<=x[i] BndU[i]=+INF
upper bound x[i]<=BndU[i] BndL[i]=-INF
range BndL[i]<=x[i]<=BndU[i] ...
free variable - BndL[I]=-INF, BndU[I]+INF
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: if constraints for all variables are same you may use minqpsetbcall()
which allows to specify constraints without using arrays.
NOTE: BndL>BndU will result in QP problem being recognized as infeasible.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetbc(const minqpstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for QP solver (all variables at once,
same constraints for all variables)
Box constraints are inactive by default (after initial creation). After
being set, they are preserved until explicitly overwritten with another
minqpsetbc() or minqpsetbcall() call, or partially overwritten with
minqpsetbci() call.
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd BndL=BndU
lower bound BndL<=x[i] BndU=+INF
upper bound x[i]<=BndU BndL=-INF
range BndL<=x[i]<=BndU ...
free variable - BndL=-INF, BndU+INF
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bound, same for all variables
BndU - upper bound, same for all variables
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: BndL>BndU will result in QP problem being recognized as infeasible.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetbcall(const minqpstate &state, const double bndl, const double bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for I-th variable (other variables are
not modified).
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd BndL=BndU
lower bound BndL<=x[i] BndU=+INF
upper bound x[i]<=BndU BndL=-INF
range BndL<=x[i]<=BndU ...
free variable - BndL=-INF, BndU+INF
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bound
BndU - upper bound
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: BndL>BndU will result in QP problem being recognized as infeasible.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetbci(const minqpstate &state, const ae_int_t i, const double bndl, const double bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets dense linear constraints for QP optimizer.
This function overrides results of previous calls to minqpsetlc(),
minqpsetlcsparse() and minqpsetlcmixed(). After call to this function
all non-box constraints are dropped, and you have only those constraints
which were specified in the present call.
If you want to specify mixed (with dense and sparse terms) linear
constraints, you should call minqpsetlcmixed().
INPUT PARAMETERS:
State - structure previously allocated with MinQPCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: linear (non-bound) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations (BLEIC-QP solver is most precise, AUL-QP
solver is less precise).
-- ALGLIB --
Copyright 19.06.2012 by Bochkanov Sergey
*************************************************************************/
void minqpsetlc(const minqpstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minqpsetlc(const minqpstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets sparse linear constraints for QP optimizer.
This function overrides results of previous calls to minqpsetlc(),
minqpsetlcsparse() and minqpsetlcmixed(). After call to this function
all non-box constraints are dropped, and you have only those constraints
which were specified in the present call.
If you want to specify mixed (with dense and sparse terms) linear
constraints, you should call minqpsetlcmixed().
INPUT PARAMETERS:
State - structure previously allocated with MinQPCreate call.
C - linear constraints, sparse matrix with dimensions at
least [K,N+1]. If matrix has larger size, only leading
Kx(N+1) rectangle is used.
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0
NOTE 1: linear (non-bound) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations (BLEIC-QP solver is most precise, AUL-QP
solver is less precise).
-- ALGLIB --
Copyright 22.08.2016 by Bochkanov Sergey
*************************************************************************/
void minqpsetlcsparse(const minqpstate &state, const sparsematrix &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets mixed linear constraints, which include a set of dense
rows, and a set of sparse rows.
This function overrides results of previous calls to minqpsetlc(),
minqpsetlcsparse() and minqpsetlcmixed().
This function may be useful if constraint matrix includes large number of
both types of rows - dense and sparse. If you have just a few sparse rows,
you may represent them in dense format without loosing performance.
Similarly, if you have just a few dense rows, you may store them in sparse
format with almost same performance.
INPUT PARAMETERS:
State - structure previously allocated with MinQPCreate call.
SparseC - linear constraints, sparse matrix with dimensions EXACTLY
EQUAL TO [SparseK,N+1]. Each row of C represents one
constraint, either equality or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
SparseCT- type of sparse constraints, array[K]:
* if SparseCT[i]>0, then I-th constraint is SparseC[i,*]*x >= SparseC[i,n+1]
* if SparseCT[i]=0, then I-th constraint is SparseC[i,*]*x = SparseC[i,n+1]
* if SparseCT[i]<0, then I-th constraint is SparseC[i,*]*x <= SparseC[i,n+1]
SparseK - number of sparse equality/inequality constraints, K>=0
DenseC - dense linear constraints, array[K,N+1].
Each row of DenseC represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of DenseC (including right part) must be finite.
DenseCT - type of constraints, array[K]:
* if DenseCT[i]>0, then I-th constraint is DenseC[i,*]*x >= DenseC[i,n+1]
* if DenseCT[i]=0, then I-th constraint is DenseC[i,*]*x = DenseC[i,n+1]
* if DenseCT[i]<0, then I-th constraint is DenseC[i,*]*x <= DenseC[i,n+1]
DenseK - number of equality/inequality constraints, DenseK>=0
NOTE 1: linear (non-box) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations (BLEIC-QP solver is most precise, AUL-QP
solver is less precise).
NOTE 2: due to backward compatibility reasons SparseC can be larger than
[SparseK,N+1]. In this case only leading [SparseK,N+1] submatrix
will be used. However, the rest of ALGLIB has more strict
requirements on the input size, so we recommend you to pass sparse
term whose size exactly matches algorithm expectations.
-- ALGLIB --
Copyright 22.08.2016 by Bochkanov Sergey
*************************************************************************/
void minqpsetlcmixed(const minqpstate &state, const sparsematrix &sparsec, const integer_1d_array &sparsect, const ae_int_t sparsek, const real_2d_array &densec, const integer_1d_array &densect, const ae_int_t densek, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides legacy API for specification of mixed dense/sparse
linear constraints.
New conventions used by ALGLIB since release 3.16.0 state that set of
sparse constraints comes first, followed by set of dense ones. This
convention is essential when you talk about things like order of Lagrange
multipliers.
However, legacy API accepted mixed constraints in reverse order. This
function is here to simplify situation with code relying on legacy API. It
simply accepts constraints in one order (old) and passes them to new API,
now in correct order.
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetlcmixedlegacy(const minqpstate &state, const real_2d_array &densec, const integer_1d_array &densect, const ae_int_t densek, const sparsematrix &sparsec, const integer_1d_array &sparsect, const ae_int_t sparsek, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets two-sided linear constraints AL <= A*x <= AU with dense
constraint matrix A.
NOTE: knowing that constraint matrix is dense helps some QP solvers
(especially modern IPM method) to utilize efficient dense Level 3
BLAS for dense parts of the problem. If your problem has both dense
and sparse constraints, you can use minqpsetlc2mixed() function,
which will result in dense algebra being applied to dense terms, and
sparse sparse linear algebra applied to sparse terms.
INPUT PARAMETERS:
State - structure previously allocated with minqpcreate() call.
A - linear constraints, array[K,N]. Each row of A represents
one constraint. One-sided inequality constraints, two-
sided inequality constraints, equality constraints are
supported (see below)
AL, AU - lower and upper bounds, array[K];
* AL[i]=AU[i] => equality constraint Ai*x
* AL[i]<AU[i] => two-sided constraint AL[i]<=Ai*x<=AU[i]
* AL[i]=-INF => one-sided constraint Ai*x<=AU[i]
* AU[i]=+INF => one-sided constraint AL[i]<=Ai*x
* AL[i]=-INF, AU[i]=+INF => constraint is ignored
K - number of equality/inequality constraints, K>=0; if not
given, inferred from sizes of A, AL, AU.
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetlc2dense(const minqpstate &state, const real_2d_array &a, const real_1d_array &al, const real_1d_array &au, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minqpsetlc2dense(const minqpstate &state, const real_2d_array &a, const real_1d_array &al, const real_1d_array &au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets two-sided linear constraints AL <= A*x <= AU with
sparse constraining matrix A. Recommended for large-scale problems.
This function overwrites linear (non-box) constraints set by previous
calls (if such calls were made).
INPUT PARAMETERS:
State - structure previously allocated with minqpcreate() call.
A - sparse matrix with size [K,N] (exactly!).
Each row of A represents one general linear constraint.
A can be stored in any sparse storage format.
AL, AU - lower and upper bounds, array[K];
* AL[i]=AU[i] => equality constraint Ai*x
* AL[i]<AU[i] => two-sided constraint AL[i]<=Ai*x<=AU[i]
* AL[i]=-INF => one-sided constraint Ai*x<=AU[i]
* AU[i]=+INF => one-sided constraint AL[i]<=Ai*x
* AL[i]=-INF, AU[i]=+INF => constraint is ignored
K - number of equality/inequality constraints, K>=0. If K=0
is specified, A, AL, AU are ignored.
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetlc2(const minqpstate &state, const sparsematrix &a, const real_1d_array &al, const real_1d_array &au, const ae_int_t k, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets two-sided linear constraints AL <= A*x <= AU with
mixed constraining matrix A including sparse part (first SparseK rows) and
dense part (last DenseK rows). Recommended for large-scale problems.
This function overwrites linear (non-box) constraints set by previous
calls (if such calls were made).
This function may be useful if constraint matrix includes large number of
both types of rows - dense and sparse. If you have just a few sparse rows,
you may represent them in dense format without loosing performance.
Similarly, if you have just a few dense rows, you may store them in sparse
format with almost same performance.
INPUT PARAMETERS:
State - structure previously allocated with minqpcreate() call.
SparseA - sparse matrix with size [K,N] (exactly!).
Each row of A represents one general linear constraint.
A can be stored in any sparse storage format.
SparseK - number of sparse constraints, SparseK>=0
DenseA - linear constraints, array[K,N], set of dense constraints.
Each row of A represents one general linear constraint.
DenseK - number of dense constraints, DenseK>=0
AL, AU - lower and upper bounds, array[SparseK+DenseK], with former
SparseK elements corresponding to sparse constraints, and
latter DenseK elements corresponding to dense constraints;
* AL[i]=AU[i] => equality constraint Ai*x
* AL[i]<AU[i] => two-sided constraint AL[i]<=Ai*x<=AU[i]
* AL[i]=-INF => one-sided constraint Ai*x<=AU[i]
* AU[i]=+INF => one-sided constraint AL[i]<=Ai*x
* AL[i]=-INF, AU[i]=+INF => constraint is ignored
K - number of equality/inequality constraints, K>=0. If K=0
is specified, A, AL, AU are ignored.
-- ALGLIB --
Copyright 01.11.2019 by Bochkanov Sergey
*************************************************************************/
void minqpsetlc2mixed(const minqpstate &state, const sparsematrix &sparsea, const ae_int_t ksparse, const real_2d_array &densea, const ae_int_t kdense, const real_1d_array &al, const real_1d_array &au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function appends two-sided linear constraint AL <= A*x <= AU to the
list of currently present dense constraints.
INPUT PARAMETERS:
State - structure previously allocated with minqpcreate() call.
A - linear constraint coefficient, array[N], right side is NOT
included.
AL, AU - lower and upper bounds;
* AL=AU => equality constraint Ai*x
* AL<AU => two-sided constraint AL<=A*x<=AU
* AL=-INF => one-sided constraint Ai*x<=AU
* AU=+INF => one-sided constraint AL<=Ai*x
* AL=-INF, AU=+INF => constraint is ignored
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minqpaddlc2dense(const minqpstate &state, const real_1d_array &a, const double al, const double au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function appends two-sided linear constraint AL <= A*x <= AU to the
list of currently present sparse constraints.
Constraint is passed in compressed format: as list of non-zero entries of
coefficient vector A. Such approach is more efficient than dense storage
for highly sparse constraint vectors.
INPUT PARAMETERS:
State - structure previously allocated with minqpcreate() call.
IdxA - array[NNZ], indexes of non-zero elements of A:
* can be unsorted
* can include duplicate indexes (corresponding entries of
ValA[] will be summed)
ValA - array[NNZ], values of non-zero elements of A
NNZ - number of non-zero coefficients in A
AL, AU - lower and upper bounds;
* AL=AU => equality constraint A*x
* AL<AU => two-sided constraint AL<=A*x<=AU
* AL=-INF => one-sided constraint A*x<=AU
* AU=+INF => one-sided constraint AL<=A*x
* AL=-INF, AU=+INF => constraint is ignored
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minqpaddlc2(const minqpstate &state, const integer_1d_array &idxa, const real_1d_array &vala, const ae_int_t nnz, const double al, const double au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function solves quadratic programming problem.
Prior to calling this function you should choose solver by means of one of
the following functions:
* minqpsetalgoquickqp() - for QuickQP solver
* minqpsetalgobleic() - for BLEIC-QP solver
* minqpsetalgodenseaul() - for Dense-AUL-QP solver
* minqpsetalgodenseipm() - for Dense-IPM-QP solver
These functions also allow you to control stopping criteria of the solver.
If you did not set solver, MinQP subpackage will automatically select
solver for your problem and will run it with default stopping criteria.
However, it is better to set explicitly solver and its stopping criteria.
INPUT PARAMETERS:
State - algorithm state
You should use MinQPResults() function to access results after calls
to this function.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey.
Special thanks to Elvira Illarionova for important suggestions on
the linearly constrained QP algorithm.
*************************************************************************/
void minqpoptimize(const minqpstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
QP solver results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution.
This array is allocated and initialized only when
Rep.TerminationType parameter is positive (success).
Rep - optimization report, contains:
* completion code in Rep.TerminationType (positive values
denote some kind of success, negative - failures)
* Lagrange multipliers - for QP solvers which support then
* other statistics
See comments on minqpreport structure for more information
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpresults(const minqpstate &state, real_1d_array &x, minqpreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
QP results
Buffered implementation of MinQPResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpresultsbuf(const minqpstate &state, real_1d_array &x, minqpreport &rep, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_REVISEDDUALSIMPLEX) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINLP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
LINEAR PROGRAMMING
The subroutine creates LP solver. After initial creation it contains
default optimization problem with zero cost vector and all variables being
fixed to zero values and no constraints.
In order to actually solve something you should:
* set cost vector with minlpsetcost()
* set variable bounds with minlpsetbc() or minlpsetbcall()
* specify constraint matrix with one of the following functions:
[*] minlpsetlc() for dense one-sided constraints
[*] minlpsetlc2dense() for dense two-sided constraints
[*] minlpsetlc2() for sparse two-sided constraints
[*] minlpaddlc2dense() to add one dense row to constraint matrix
[*] minlpaddlc2() to add one row to constraint matrix (compressed format)
* call minlpoptimize() to run the solver and minlpresults() to get the
solution vector and additional information.
Presently this optimizer supports only revised simplex method as
underlying solver. DSE pricing and bounds flipping ratio test (aka long
dual step) are supported. Large-scale sparse LU solver with Forest-Tomlin
is used internally as linear algebra driver.
Future releases of ALGLIB may introduce other solvers.
INPUT PARAMETERS:
N - problem size
OUTPUT PARAMETERS:
State - optimizer in the default state
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpcreate(const ae_int_t n, minlpstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets cost term for LP solver.
By default, cost term is zero.
INPUT PARAMETERS:
State - structure which stores algorithm state
C - cost term, array[N].
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetcost(const minlpstate &state, const real_1d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients.
ALGLIB optimizers use scaling matrices to test stopping conditions and as
preconditioner.
Scale of the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the
function
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetscale(const minlpstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for LP solver (all variables at once,
different constraints for different variables).
The default state of constraints is to have all variables fixed at zero.
You have to overwrite it by your own constraint vector. Constraint status
is preserved until constraints are explicitly overwritten with another
minlpsetbc() call, overwritten with minlpsetbcall(), or partially
overwritten with minlmsetbci() call.
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd[i] BndL[i]=BndU[i]
lower bound BndL[i]<=x[i] BndU[i]=+INF
upper bound x[i]<=BndU[i] BndL[i]=-INF
range BndL[i]<=x[i]<=BndU[i] ...
free variable - BndL[I]=-INF, BndU[I]+INF
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
BndU - upper bounds, array[N].
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: if constraints for all variables are same you may use minlpsetbcall()
which allows to specify constraints without using arrays.
NOTE: BndL>BndU will result in LP problem being recognized as infeasible.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetbc(const minlpstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for LP solver (all variables at once,
same constraints for all variables)
The default state of constraints is to have all variables fixed at zero.
You have to overwrite it by your own constraint vector. Constraint status
is preserved until constraints are explicitly overwritten with another
minlpsetbc() call or partially overwritten with minlpsetbcall().
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd[i] BndL[i]=BndU[i]
lower bound BndL[i]<=x[i] BndU[i]=+INF
upper bound x[i]<=BndU[i] BndL[i]=-INF
range BndL[i]<=x[i]<=BndU[i] ...
free variable - BndL[I]=-INF, BndU[I]+INF
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bound, same for all variables
BndU - upper bound, same for all variables
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: minlpsetbc() can be used to specify different constraints for
different variables.
NOTE: BndL>BndU will result in LP problem being recognized as infeasible.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetbcall(const minlpstate &state, const double bndl, const double bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets box constraints for I-th variable (other variables are
not modified).
The default state of constraints is to have all variables fixed at zero.
You have to overwrite it by your own constraint vector.
Following types of constraints are supported:
DESCRIPTION CONSTRAINT HOW TO SPECIFY
fixed variable x[i]=Bnd[i] BndL[i]=BndU[i]
lower bound BndL[i]<=x[i] BndU[i]=+INF
upper bound x[i]<=BndU[i] BndL[i]=-INF
range BndL[i]<=x[i]<=BndU[i] ...
free variable - BndL[I]=-INF, BndU[I]+INF
INPUT PARAMETERS:
State - structure stores algorithm state
I - variable index, in [0,N)
BndL - lower bound for I-th variable
BndU - upper bound for I-th variable
NOTE: infinite values can be specified by means of Double.PositiveInfinity
and Double.NegativeInfinity (in C#) and alglib::fp_posinf and
alglib::fp_neginf (in C++).
NOTE: you may replace infinities by very small/very large values, but it
is not recommended because large numbers may introduce large numerical
errors in the algorithm.
NOTE: minlpsetbc() can be used to specify different constraints for
different variables.
NOTE: BndL>BndU will result in LP problem being recognized as infeasible.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetbci(const minlpstate &state, const ae_int_t i, const double bndl, const double bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets one-sided linear constraints A*x ~ AU, where "~" can be
a mix of "<=", "=" and ">=".
IMPORTANT: this function is provided here for compatibility with the rest
of ALGLIB optimizers which accept constraints in format like
this one. Many real-life problems feature two-sided constraints
like a0 <= a*x <= a1. It is really inefficient to add them as a
pair of one-sided constraints.
Use minlpsetlc2dense(), minlpsetlc2(), minlpaddlc2() (or its
sparse version) wherever possible.
INPUT PARAMETERS:
State - structure previously allocated with minlpcreate() call.
A - linear constraints, array[K,N+1]. Each row of A represents
one constraint, with first N elements being linear coefficients,
and last element being right side.
CT - constraint types, array[K]:
* if CT[i]>0, then I-th constraint is A[i,*]*x >= A[i,n]
* if CT[i]=0, then I-th constraint is A[i,*]*x = A[i,n]
* if CT[i]<0, then I-th constraint is A[i,*]*x <= A[i,n]
K - number of equality/inequality constraints, K>=0; if not
given, inferred from sizes of A and CT.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetlc(const minlpstate &state, const real_2d_array &a, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minlpsetlc(const minlpstate &state, const real_2d_array &a, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets two-sided linear constraints AL <= A*x <= AU.
This version accepts dense matrix as input; internally LP solver uses
sparse storage anyway (most LP problems are sparse), but for your
convenience it may accept dense inputs. This function overwrites linear
constraints set by previous calls (if such calls were made).
We recommend you to use sparse version of this function unless you solve
small-scale LP problem (less than few hundreds of variables).
NOTE: there also exist several versions of this function:
* one-sided dense version which accepts constraints in the same
format as one used by QP and NLP solvers
* two-sided sparse version which accepts sparse matrix
* two-sided dense version which allows you to add constraints row by row
* two-sided sparse version which allows you to add constraints row by row
INPUT PARAMETERS:
State - structure previously allocated with minlpcreate() call.
A - linear constraints, array[K,N]. Each row of A represents
one constraint. One-sided inequality constraints, two-
sided inequality constraints, equality constraints are
supported (see below)
AL, AU - lower and upper bounds, array[K];
* AL[i]=AU[i] => equality constraint Ai*x
* AL[i]<AU[i] => two-sided constraint AL[i]<=Ai*x<=AU[i]
* AL[i]=-INF => one-sided constraint Ai*x<=AU[i]
* AU[i]=+INF => one-sided constraint AL[i]<=Ai*x
* AL[i]=-INF, AU[i]=+INF => constraint is ignored
K - number of equality/inequality constraints, K>=0; if not
given, inferred from sizes of A, AL, AU.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetlc2dense(const minlpstate &state, const real_2d_array &a, const real_1d_array &al, const real_1d_array &au, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minlpsetlc2dense(const minlpstate &state, const real_2d_array &a, const real_1d_array &al, const real_1d_array &au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets two-sided linear constraints AL <= A*x <= AU with
sparse constraining matrix A. Recommended for large-scale problems.
This function overwrites linear (non-box) constraints set by previous
calls (if such calls were made).
INPUT PARAMETERS:
State - structure previously allocated with minlpcreate() call.
A - sparse matrix with size [K,N] (exactly!).
Each row of A represents one general linear constraint.
A can be stored in any sparse storage format.
AL, AU - lower and upper bounds, array[K];
* AL[i]=AU[i] => equality constraint Ai*x
* AL[i]<AU[i] => two-sided constraint AL[i]<=Ai*x<=AU[i]
* AL[i]=-INF => one-sided constraint Ai*x<=AU[i]
* AU[i]=+INF => one-sided constraint AL[i]<=Ai*x
* AL[i]=-INF, AU[i]=+INF => constraint is ignored
K - number of equality/inequality constraints, K>=0. If K=0
is specified, A, AL, AU are ignored.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpsetlc2(const minlpstate &state, const sparsematrix &a, const real_1d_array &al, const real_1d_array &au, const ae_int_t k, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function appends two-sided linear constraint AL <= A*x <= AU to the
list of currently present constraints.
This version accepts dense constraint vector as input, but sparsifies it
for internal storage and processing. Thus, time to add one constraint in
is O(N) - we have to scan entire array of length N. Sparse version of this
function is order of magnitude faster for constraints with just a few
nonzeros per row.
INPUT PARAMETERS:
State - structure previously allocated with minlpcreate() call.
A - linear constraint coefficient, array[N], right side is NOT
included.
AL, AU - lower and upper bounds;
* AL=AU => equality constraint Ai*x
* AL<AU => two-sided constraint AL<=A*x<=AU
* AL=-INF => one-sided constraint Ai*x<=AU
* AU=+INF => one-sided constraint AL<=Ai*x
* AL=-INF, AU=+INF => constraint is ignored
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpaddlc2dense(const minlpstate &state, const real_1d_array &a, const double al, const double au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function appends two-sided linear constraint AL <= A*x <= AU to the
list of currently present constraints.
Constraint is passed in compressed format: as list of non-zero entries of
coefficient vector A. Such approach is more efficient than dense storage
for highly sparse constraint vectors.
INPUT PARAMETERS:
State - structure previously allocated with minlpcreate() call.
IdxA - array[NNZ], indexes of non-zero elements of A:
* can be unsorted
* can include duplicate indexes (corresponding entries of
ValA[] will be summed)
ValA - array[NNZ], values of non-zero elements of A
NNZ - number of non-zero coefficients in A
AL, AU - lower and upper bounds;
* AL=AU => equality constraint A*x
* AL<AU => two-sided constraint AL<=A*x<=AU
* AL=-INF => one-sided constraint A*x<=AU
* AU=+INF => one-sided constraint AL<=A*x
* AL=-INF, AU=+INF => constraint is ignored
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey
*************************************************************************/
void minlpaddlc2(const minlpstate &state, const integer_1d_array &idxa, const real_1d_array &vala, const ae_int_t nnz, const double al, const double au, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function solves LP problem.
INPUT PARAMETERS:
State - algorithm state
You should use minlpresults() function to access results after calls to
this function.
-- ALGLIB --
Copyright 19.07.2018 by Bochkanov Sergey.
*************************************************************************/
void minlpoptimize(const minlpstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
LP solver results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[N], solution. Filled by zeros on failure.
Rep - optimization report. You should check Rep.TerminationType,
which contains completion code, and you may check another
fields which contain another information about algorithm
functioning.
Failure codes returned by algorithm are:
* -4 LP problem is primal unbounded (dual infeasible)
* -3 LP problem is primal infeasible (dual unbounded)
Success codes:
* 1..4 successful completion
* 5 MaxIts steps was taken
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlpresults(const minlpstate &state, real_1d_array &x, minlpreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
LP results
Buffered implementation of MinLPResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlpresultsbuf(const minlpstate &state, real_1d_array &x, minlpreport &rep, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_NLCSLP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MINNLC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
NONLINEARLY CONSTRAINED OPTIMIZATION
WITH PRECONDITIONED AUGMENTED LAGRANGIAN ALGORITHM
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
* nonlinear equality constraints Gi(x)=0
* nonlinear inequality constraints Hi(x)<=0
REQUIREMENTS:
* user must provide function value and gradient for F(), H(), G()
* starting point X0 must be feasible or not too far away from the feasible
set
* F(), G(), H() are continuously differentiable on the feasible set and
its neighborhood
* nonlinear constraints G() and H() must have non-zero gradient at G(x)=0
and at H(x)=0. Say, constraint like x^2>=1 is supported, but x^2>=0 is
NOT supported.
USAGE:
Constrained optimization if far more complex than the unconstrained one.
Nonlinearly constrained optimization is one of the most esoteric numerical
procedures.
Here we give very brief outline of the MinNLC optimizer. We strongly
recommend you to study examples in the ALGLIB Reference Manual and to read
ALGLIB User Guide on optimization, which is available at
http://www.alglib.net/optimization/
1. User initializes algorithm state with MinNLCCreate() call and chooses
what NLC solver to use. There is some solver which is used by default,
with default settings, but you should NOT rely on default choice. It
may change in future releases of ALGLIB without notice, and no one can
guarantee that new solver will be able to solve your problem with
default settings.
From the other side, if you choose solver explicitly, you can be pretty
sure that it will work with new ALGLIB releases.
In the current release following solvers can be used:
* SQP solver, recommended for medium-scale problems (less than thousand
of variables) with hard-to-evaluate target functions. Requires less
function evaluations than other solvers but each step involves
solution of QP subproblem, so running time may be higher than that of
AUL (another recommended option). Activated with minnlcsetalgosqp()
function.
* AUL solver with dense preconditioner, recommended for large-scale
problems or for problems with cheap target function. Needs more
function evaluations that SQP (about 5x-10x times more), but its
iterations are much cheaper that that of SQP. Activated with
minnlcsetalgoaul() function.
* SLP solver, successive linear programming. The slowest one, requires
more target function evaluations that SQP and AUL. However, it is
somewhat more robust in tricky cases, so it can be used as a backup
plan. Activated with minnlcsetalgoslp() function.
2. [optional] user activates OptGuard integrity checker which tries to
detect possible errors in the user-supplied callbacks:
* discontinuity/nonsmoothness of the target/nonlinear constraints
* errors in the analytic gradient provided by user
This feature is essential for early prototyping stages because it helps
to catch common coding and problem statement errors.
OptGuard can be activated with following functions (one per each check
performed):
* minnlcoptguardsmoothness()
* minnlcoptguardgradient()
3. User adds boundary and/or linear and/or nonlinear constraints by means
of calling one of the following functions:
a) minnlcsetbc() for boundary constraints
b) minnlcsetlc() for linear constraints
c) minnlcsetnlc() for nonlinear constraints
You may combine (a), (b) and (c) in one optimization problem.
4. User sets scale of the variables with minnlcsetscale() function. It is
VERY important to set scale of the variables, because nonlinearly
constrained problems are hard to solve when variables are badly scaled.
5. User sets stopping conditions with minnlcsetcond(). If NLC solver
uses inner/outer iteration layout, this function sets stopping
conditions for INNER iterations.
6. Finally, user calls minnlcoptimize() function which takes algorithm
state and pointer (delegate, etc.) to callback function which calculates
F/G/H.
7. User calls minnlcresults() to get solution; additionally you can
retrieve OptGuard report with minnlcoptguardresults(), and get detailed
report about purported errors in the target function with:
* minnlcoptguardnonc1test0results()
* minnlcoptguardnonc1test1results()
8. Optionally user may call minnlcrestartfrom() to solve another problem
with same N but another starting point. minnlcrestartfrom() allows to
reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlccreate(const ae_int_t n, const real_1d_array &x, minnlcstate &state, const xparams _xparams = alglib::xdefault);
void minnlccreate(const real_1d_array &x, minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine is a finite difference variant of MinNLCCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinNLCCreate() in order to get more
information about creation of NLC optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinNLCSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large TRUNCATION errors, while too small
step will result in too large NUMERICAL errors. 1.0E-4 can be good
value to start from.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. Imprecise gradient may slow down
convergence, especially on highly nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlccreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minnlcstate &state, const xparams _xparams = alglib::xdefault);
void minnlccreatef(const real_1d_array &x, const double diffstep, minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets boundary constraints for NLC optimizer.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinNLCRestartFrom().
You may combine boundary constraints with general linear ones - and with
nonlinear ones! Boundary constraints are handled more efficiently than
other types. Thus, if your problem has mixed constraints, you may
explicitly specify some of them as boundary and save some time/space.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: when you solve your problem with augmented Lagrangian solver,
boundary constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetbc(const minnlcstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets linear constraints for MinNLC optimizer.
Linear constraints are inactive by default (after initial creation). They
are preserved after algorithm restart with MinNLCRestartFrom().
You may combine linear constraints with boundary ones - and with nonlinear
ones! If your problem has mixed constraints, you may explicitly specify
some of them as linear. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE 1: when you solve your problem with augmented Lagrangian solver,
linear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetlc(const minnlcstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minnlcsetlc(const minnlcstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets nonlinear constraints for MinNLC optimizer.
In fact, this function sets NUMBER of nonlinear constraints. Constraints
itself (constraint functions) are passed to MinNLCOptimize() method. This
method requires user-defined vector function F[] and its Jacobian J[],
where:
* first component of F[] and first row of Jacobian J[] corresponds to
function being minimized
* next NLEC components of F[] (and rows of J) correspond to nonlinear
equality constraints G_i(x)=0
* next NLIC components of F[] (and rows of J) correspond to nonlinear
inequality constraints H_i(x)<=0
NOTE: you may combine nonlinear constraints with linear/boundary ones. If
your problem has mixed constraints, you may explicitly specify some
of them as linear ones. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
NLEC - number of Non-Linear Equality Constraints (NLEC), >=0
NLIC - number of Non-Linear Inquality Constraints (NLIC), >=0
NOTE 1: when you solve your problem with augmented Lagrangian solver,
nonlinear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
feasible area!
NOTE 2: algorithm scales variables according to scale specified by
MinNLCSetScale() function, so it can handle problems with badly
scaled variables (as long as we KNOW their scales).
However, there is no way to automatically scale nonlinear
constraints Gi(x) and Hi(x). Inappropriate scaling of Gi/Hi may
ruin convergence. Solving problem with constraint "1000*G0(x)=0"
is NOT same as solving it with constraint "0.001*G0(x)=0".
It means that YOU are the one who is responsible for correct
scaling of nonlinear constraints Gi(x) and Hi(x). We recommend you
to scale nonlinear constraints in such way that I-th component of
dG/dX (or dH/dx) has approximately unit magnitude (for problems
with unit scale) or has magnitude approximately equal to 1/S[i]
(where S is a scale set by MinNLCSetScale() function).
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetnlc(const minnlcstate &state, const ae_int_t nlec, const ae_int_t nlic, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for inner iterations of optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinNLCSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
selection of the stopping condition.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetcond(const minnlcstate &state, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for NLC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetscale(const minnlcstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets preconditioner to "inexact LBFGS-based" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may use following preconditioners, each with its own
benefits and drawbacks:
a) inexact LBFGS-based, with O(N*K) evaluation time
b) exact low rank one, with O(N*K^2) evaluation time
c) exact robust one, with O(N^3+K*N^2) evaluation time
where K is a total number of general linear and nonlinear constraints (box
ones are not counted).
Inexact LBFGS-based preconditioner uses L-BFGS formula combined with
orthogonality assumption to perform very fast updates. For a N-dimensional
problem with K general linear or nonlinear constraints (boundary ones are
not counted) it has O(N*K) cost per iteration. This preconditioner has
best quality (less iterations) when general linear and nonlinear
constraints are orthogonal to each other (orthogonality with respect to
boundary constraints is not required). Number of iterations increases when
constraints are non-orthogonal, because algorithm assumes orthogonality,
but still it is better than no preconditioner at all.
INPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecinexact(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets preconditioner to "exact low rank" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may use following preconditioners, each with its own
benefits and drawbacks:
a) inexact LBFGS-based, with O(N*K) evaluation time
b) exact low rank one, with O(N*K^2) evaluation time
c) exact robust one, with O(N^3+K*N^2) evaluation time
where K is a total number of general linear and nonlinear constraints (box
ones are not counted).
It also provides special unpreconditioned mode of operation which can be
used for test purposes. Comments below discuss low rank preconditioner.
Exact low-rank preconditioner uses Woodbury matrix identity to build
quadratic model of the penalized function. It has following features:
* no special assumptions about orthogonality of constraints
* preconditioner evaluation is optimized for K<<N. Its cost is O(N*K^2),
so it may become prohibitively slow for K>=N.
* finally, stability of the process is guaranteed only for K<<N. Woodbury
update often fail for K>=N due to degeneracy of intermediate matrices.
That's why we recommend to use "exact robust" preconditioner for such
cases.
RECOMMENDATIONS
We recommend to choose between "exact low rank" and "exact robust"
preconditioners, with "low rank" version being chosen when you know in
advance that total count of non-box constraints won't exceed N, and "robust"
version being chosen when you need bulletproof solution.
INPUT PARAMETERS:
State - structure stores algorithm state
UpdateFreq- update frequency. Preconditioner is rebuilt after every
UpdateFreq iterations. Recommended value: 10 or higher.
Zero value means that good default value will be used.
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecexactlowrank(const minnlcstate &state, const ae_int_t updatefreq, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets preconditioner to "exact robust" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may use following preconditioners, each with its own
benefits and drawbacks:
a) inexact LBFGS-based, with O(N*K) evaluation time
b) exact low rank one, with O(N*K^2) evaluation time
c) exact robust one, with O(N^3+K*N^2) evaluation time
where K is a total number of general linear and nonlinear constraints (box
ones are not counted).
It also provides special unpreconditioned mode of operation which can be
used for test purposes. Comments below discuss robust preconditioner.
Exact robust preconditioner uses Cholesky decomposition to invert
approximate Hessian matrix H=D+W'*C*W (where D stands for diagonal terms
of Hessian, combined result of initial scaling matrix and penalty from box
constraints; W stands for general linear constraints and linearization of
nonlinear ones; C stands for diagonal matrix of penalty coefficients).
This preconditioner has following features:
* no special assumptions about constraint structure
* preconditioner is optimized for stability; unlike "exact low rank"
version which fails for K>=N, this one works well for any value of K.
* the only drawback is that is takes O(N^3+K*N^2) time to build it. No
economical Woodbury update is applied even when it makes sense, thus
there are exist situations (K<<N) when "exact low rank" preconditioner
outperforms this one.
RECOMMENDATIONS
We recommend to choose between "exact low rank" and "exact robust"
preconditioners, with "low rank" version being chosen when you know in
advance that total count of non-box constraints won't exceed N, and "robust"
version being chosen when you need bulletproof solution.
INPUT PARAMETERS:
State - structure stores algorithm state
UpdateFreq- update frequency. Preconditioner is rebuilt after every
UpdateFreq iterations. Recommended value: 10 or higher.
Zero value means that good default value will be used.
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecexactrobust(const minnlcstate &state, const ae_int_t updatefreq, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets preconditioner to "turned off" mode.
Preconditioning is very important for convergence of Augmented Lagrangian
algorithm because presence of penalty term makes problem ill-conditioned.
Difference between performance of preconditioned and unpreconditioned
methods can be as large as 100x!
MinNLC optimizer may utilize two preconditioners, each with its own
benefits and drawbacks: a) inexact LBFGS-based, and b) exact low rank one.
It also provides special unpreconditioned mode of operation which can be
used for test purposes.
This function activates this test mode. Do not use it in production code
to solve real-life problems.
INPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 26.09.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetprecnone(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length (after scaling of step vector with
respect to variable scales specified by minnlcsetscale() call).
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0 (default), if
you don't want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
NOTE: different solvers employed by MinNLC optimizer use different norms
for step; AUL solver uses 2-norm, whilst SLP solver uses INF-norm.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcsetstpmax(const minnlcstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells MinNLC unit to use Augmented Lagrangian algorithm
for nonlinearly constrained optimization. This algorithm is a slight
modification of one described in "A Modified Barrier-Augmented Lagrangian
Method for Constrained Minimization (1999)" by D.GOLDFARB, R.POLYAK,
K. SCHEINBERG, I.YUZEFOVICH.
AUL solver can be significantly faster than SQP on easy problems due to
cheaper iterations, although it needs more function evaluations.
Augmented Lagrangian algorithm works by converting problem of minimizing
F(x) subject to equality/inequality constraints to unconstrained problem
of the form
min[ f(x) +
+ Rho*PENALTY_EQ(x) + SHIFT_EQ(x,Nu1) +
+ Rho*PENALTY_INEQ(x) + SHIFT_INEQ(x,Nu2) ]
where:
* Rho is a fixed penalization coefficient
* PENALTY_EQ(x) is a penalty term, which is used to APPROXIMATELY enforce
equality constraints
* SHIFT_EQ(x) is a special "shift" term which is used to "fine-tune"
equality constraints, greatly increasing precision
* PENALTY_INEQ(x) is a penalty term which is used to approximately enforce
inequality constraints
* SHIFT_INEQ(x) is a special "shift" term which is used to "fine-tune"
inequality constraints, greatly increasing precision
* Nu1/Nu2 are vectors of Lagrange coefficients which are fine-tuned during
outer iterations of algorithm
This version of AUL algorithm uses preconditioner, which greatly
accelerates convergence. Because this algorithm is similar to penalty
methods, it may perform steps into infeasible area. All kinds of
constraints (boundary, linear and nonlinear ones) may be violated in
intermediate points - and in the solution. However, properly configured
AUL method is significantly better at handling constraints than barrier
and/or penalty methods.
The very basic outline of algorithm is given below:
1) first outer iteration is performed with "default" values of Lagrange
multipliers Nu1/Nu2. Solution quality is low (candidate point can be
too far away from true solution; large violation of constraints is
possible) and is comparable with that of penalty methods.
2) subsequent outer iterations refine Lagrange multipliers and improve
quality of the solution.
INPUT PARAMETERS:
State - structure which stores algorithm state
Rho - penalty coefficient, Rho>0:
* large enough that algorithm converges with desired
precision. Minimum value is 10*max(S'*diag(H)*S), where
S is a scale matrix (set by MinNLCSetScale) and H is a
Hessian of the function being minimized. If you can not
easily estimate Hessian norm, see our recommendations
below.
* not TOO large to prevent ill-conditioning
* for unit-scale problems (variables and Hessian have unit
magnitude), Rho=100 or Rho=1000 can be used.
* it is important to note that Rho is internally multiplied
by scaling matrix, i.e. optimum value of Rho depends on
scale of variables specified by MinNLCSetScale().
ItsCnt - number of outer iterations:
* ItsCnt=0 means that small number of outer iterations is
automatically chosen (10 iterations in current version).
* ItsCnt=1 means that AUL algorithm performs just as usual
barrier method.
* ItsCnt>1 means that AUL algorithm performs specified
number of outer iterations
HOW TO CHOOSE PARAMETERS
Nonlinear optimization is a tricky area and Augmented Lagrangian algorithm
is sometimes hard to tune. Good values of Rho and ItsCnt are problem-
specific. In order to help you we prepared following set of
recommendations:
* for unit-scale problems (variables and Hessian have unit magnitude),
Rho=100 or Rho=1000 can be used.
* start from some small value of Rho and solve problem with just one
outer iteration (ItcCnt=1). In this case algorithm behaves like penalty
method. Increase Rho in 2x or 10x steps until you see that one outer
iteration returns point which is "rough approximation to solution".
It is very important to have Rho so large that penalty term becomes
constraining i.e. modified function becomes highly convex in constrained
directions.
From the other side, too large Rho may prevent you from converging to
the solution. You can diagnose it by studying number of inner iterations
performed by algorithm: too few (5-10 on 1000-dimensional problem) or
too many (orders of magnitude more than dimensionality) usually means
that Rho is too large.
* with just one outer iteration you usually have low-quality solution.
Some constraints can be violated with very large margin, while other
ones (which are NOT violated in the true solution) can push final point
too far in the inner area of the feasible set.
For example, if you have constraint x0>=0 and true solution x0=1, then
merely a presence of "x0>=0" will introduce a bias towards larger values
of x0. Say, algorithm may stop at x0=1.5 instead of 1.0.
* after you found good Rho, you may increase number of outer iterations.
ItsCnt=10 is a good value. Subsequent outer iteration will refine values
of Lagrange multipliers. Constraints which were violated will be
enforced, inactive constraints will be dropped (corresponding multipliers
will be decreased). Ideally, you should see 10-1000x improvement in
constraint handling (constraint violation is reduced).
* if you see that algorithm converges to vicinity of solution, but
additional outer iterations do not refine solution, it may mean that
algorithm is unstable - it wanders around true solution, but can not
approach it. Sometimes algorithm may be stabilized by increasing Rho one
more time, making it 5x or 10x larger.
SCALING OF CONSTRAINTS [IMPORTANT]
AUL optimizer scales variables according to scale specified by
MinNLCSetScale() function, so it can handle problems with badly scaled
variables (as long as we KNOW their scales). However, because function
being optimized is a mix of original function and constraint-dependent
penalty functions, it is important to rescale both variables AND
constraints.
Say, if you minimize f(x)=x^2 subject to 1000000*x>=0, then you have
constraint whose scale is different from that of target function (another
example is 0.000001*x>=0). It is also possible to have constraints whose
scales are misaligned: 1000000*x0>=0, 0.000001*x1<=0. Inappropriate
scaling may ruin convergence because minimizing x^2 subject to x>=0 is NOT
same as minimizing it subject to 1000000*x>=0.
Because we know coefficients of boundary/linear constraints, we can
automatically rescale and normalize them. However, there is no way to
automatically rescale nonlinear constraints Gi(x) and Hi(x) - they are
black boxes.
It means that YOU are the one who is responsible for correct scaling of
nonlinear constraints Gi(x) and Hi(x). We recommend you to rescale
nonlinear constraints in such way that I-th component of dG/dX (or dH/dx)
has magnitude approximately equal to 1/S[i] (where S is a scale set by
MinNLCSetScale() function).
WHAT IF IT DOES NOT CONVERGE?
It is possible that AUL algorithm fails to converge to precise values of
Lagrange multipliers. It stops somewhere around true solution, but candidate
point is still too far from solution, and some constraints are violated.
Such kind of failure is specific for Lagrangian algorithms - technically,
they stop at some point, but this point is not constrained solution.
There are exist several reasons why algorithm may fail to converge:
a) too loose stopping criteria for inner iteration
b) degenerate, redundant constraints
c) target function has unconstrained extremum exactly at the boundary of
some constraint
d) numerical noise in the target function
In all these cases algorithm is unstable - each outer iteration results in
large and almost random step which improves handling of some constraints,
but violates other ones (ideally outer iterations should form a sequence
of progressively decreasing steps towards solution).
First reason possible is that too loose stopping criteria for inner
iteration were specified. Augmented Lagrangian algorithm solves a sequence
of intermediate problems, and requries each of them to be solved with high
precision. Insufficient precision results in incorrect update of Lagrange
multipliers.
Another reason is that you may have specified degenerate constraints: say,
some constraint was repeated twice. In most cases AUL algorithm gracefully
handles such situations, but sometimes it may spend too much time figuring
out subtle degeneracies in constraint matrix.
Third reason is tricky and hard to diagnose. Consider situation when you
minimize f=x^2 subject to constraint x>=0. Unconstrained extremum is
located exactly at the boundary of constrained area. In this case
algorithm will tend to oscillate between negative and positive x. Each
time it stops at x<0 it "reinforces" constraint x>=0, and each time it is
bounced to x>0 it "relaxes" constraint (and is attracted to x<0).
Such situation sometimes happens in problems with hidden symetries.
Algorithm is got caught in a loop with Lagrange multipliers being
continuously increased/decreased. Luckily, such loop forms after at least
three iterations, so this problem can be solved by DECREASING number of
outer iterations down to 1-2 and increasing penalty coefficient Rho as
much as possible.
Final reason is numerical noise. AUL algorithm is robust against moderate
noise (more robust than, say, active set methods), but large noise may
destabilize algorithm.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcsetalgoaul(const minnlcstate &state, const double rho, const ae_int_t itscnt, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells MinNLC optimizer to use SLP (Successive Linear
Programming) algorithm for nonlinearly constrained optimization. This
algorithm is a slight modification of one described in "A Linear
programming-based optimization algorithm for solving nonlinear programming
problems" (2010) by Claus Still and Tapio Westerlund.
This solver is the slowest one in ALGLIB, it requires more target function
evaluations that SQP and AUL. However it is somewhat more robust in tricky
cases, so it can be used as a backup plan. We recommend to use this algo
when SQP/AUL do not work (does not return the solution you expect). If
trying different approach gives same results, then MAYBE something is
wrong with your optimization problem.
Despite its name ("linear" = "first order method") this algorithm performs
steps similar to that of conjugate gradients method; internally it uses
orthogonality/conjugacy requirement for subsequent steps which makes it
closer to second order methods in terms of convergence speed.
Convergence is proved for the following case:
* function and constraints are continuously differentiable (C1 class)
* extended Mangasarian–Fromovitz constraint qualification (EMFCQ) holds;
in the context of this algorithm EMFCQ means that one can, for any
infeasible point, find a search direction such that the constraint
infeasibilities are reduced.
This algorithm has following nice properties:
* no parameters to tune
* no convexity requirements for target function or constraints
* initial point can be infeasible
* algorithm respects box constraints in all intermediate points (it does
not even evaluate function outside of box constrained area)
* once linear constraints are enforced, algorithm will not violate them
* no such guarantees can be provided for nonlinear constraints, but once
nonlinear constraints are enforced, algorithm will try to respect them
as much as possible
* numerical differentiation does not violate box constraints (although
general linear and nonlinear ones can be violated during differentiation)
* from our experience, this algorithm is somewhat more robust in really
difficult cases
INPUT PARAMETERS:
State - structure which stores algorithm state
===== TRACING SLP SOLVER =================================================
SLP solver supports advanced tracing capabilities. You can trace algorithm
output by specifying following trace symbols (case-insensitive) by means
of trace_file() call:
* 'SLP' - for basic trace of algorithm steps and decisions. Only
short scalars (function values and deltas) are printed.
N-dimensional quantities like search directions are NOT
printed.
It also prints OptGuard integrity checker report when
nonsmoothness of target/constraints is suspected.
* 'SLP.DETAILED'- for output of points being visited and search directions
This symbol also implicitly defines 'SLP'. You can
control output format by additionally specifying:
* nothing to output in 6-digit exponential format
* 'PREC.E15' to output in 15-digit exponential format
* 'PREC.F6' to output in 6-digit fixed-point format
* 'SLP.PROBING' - to let algorithm insert additional function evaluations
before line search in order to build human-readable
chart of the raw Lagrangian (~40 additional function
evaluations is performed for each line search). This
symbol also implicitly defines 'SLP'.
* 'OPTGUARD' - for report of smoothness/continuity violations in target
and/or constraints. This kind of reporting is included
in 'SLP', but it comes with lots of additional info. If
you need just smoothness monitoring, specify this
setting.
NOTE: this tag merely directs OptGuard output to log
file. Even if you specify it, you still have to
configure OptGuard by calling minnlcoptguard...()
family of functions.
By default trace is disabled and adds no overhead to the optimization
process. However, specifying any of the symbols adds some formatting and
output-related overhead. Specifying 'SLP.PROBING' adds even larger
overhead due to additional function evaluations being performed.
You may specify multiple symbols by separating them with commas:
>
> alglib::trace_file("SLP,SLP.PROBING,PREC.F6", "path/to/trace.log")
>
-- ALGLIB --
Copyright 02.04.2018 by Bochkanov Sergey
*************************************************************************/
void minnlcsetalgoslp(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells MinNLC optimizer to use SQP (Successive Quadratic
Programming) algorithm for nonlinearly constrained optimization.
This algorithm needs order of magnitude (5x-10x) less function evaluations
than AUL solver, but has higher overhead because each iteration involves
solution of quadratic programming problem.
Convergence is proved for the following case:
* function and constraints are continuously differentiable (C1 class)
This algorithm has following nice properties:
* no parameters to tune
* no convexity requirements for target function or constraints
* initial point can be infeasible
* algorithm respects box constraints in all intermediate points (it does
not even evaluate function outside of box constrained area)
* once linear constraints are enforced, algorithm will not violate them
* no such guarantees can be provided for nonlinear constraints, but once
nonlinear constraints are enforced, algorithm will try to respect them
as much as possible
* numerical differentiation does not violate box constraints (although
general linear and nonlinear ones can be violated during differentiation)
We recommend this algorithm as a default option for medium-scale problems
(less than thousand of variables) or problems with target function being
hard to evaluate.
For large-scale problems or ones with very cheap target function
AUL solver can be better option.
INPUT PARAMETERS:
State - structure which stores algorithm state
===== INTERACTION WITH OPTGUARD ==========================================
OptGuard integrity checker allows us to catch problems like errors in
gradients and discontinuity/nonsmoothness of the target/constraints.
Latter kind of problems can be detected by looking upon line searches
performed during optimization and searching for signs of nonsmoothness.
The problem with SQP is that it is too good for OptGuard to work - it does
not perform line searches. It typically needs 1-2 function evaluations
per step, and it is not enough for OptGuard to detect nonsmoothness.
So, if you suspect that your problem is nonsmooth, we recommend you to use
AUL or SLP solvers.
===== TRACING SQP SOLVER =================================================
SQP solver supports advanced tracing capabilities. You can trace algorithm
output by specifying following trace symbols (case-insensitive) by means
of trace_file() call:
* 'SQP' - for basic trace of algorithm steps and decisions. Only
short scalars (function values and deltas) are printed.
N-dimensional quantities like search directions are NOT
printed.
It also prints OptGuard integrity checker report when
nonsmoothness of target/constraints is suspected.
* 'SQP.DETAILED'- for output of points being visited and search directions
This symbol also implicitly defines 'SQP'. You can
control output format by additionally specifying:
* nothing to output in 6-digit exponential format
* 'PREC.E15' to output in 15-digit exponential format
* 'PREC.F6' to output in 6-digit fixed-point format
* 'SQP.PROBING' - to let algorithm insert additional function evaluations
before line search in order to build human-readable
chart of the raw Lagrangian (~40 additional function
evaluations is performed for each line search). This
symbol also implicitly defines 'SQP'.
By default trace is disabled and adds no overhead to the optimization
process. However, specifying any of the symbols adds some formatting and
output-related overhead. Specifying 'SQP.PROBING' adds even larger
overhead due to additional function evaluations being performed.
You may specify multiple symbols by separating them with commas:
>
> alglib::trace_file("SQP,SQP.PROBING,PREC.F6", "path/to/trace.log")
>
-- ALGLIB --
Copyright 02.12.2019 by Bochkanov Sergey
*************************************************************************/
void minnlcsetalgosqp(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinNLCOptimize().
NOTE: algorithm passes two parameters to rep() callback - current point
and penalized function value at current point. Important - function
value which is returned is NOT function being minimized. It is sum
of the value of the function being minimized - and penalty term.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcsetxrep(const minnlcstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minnlciteration(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied Jacobian, and one which uses only function
vector and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
you should choose appropriate variant of MinNLCOptimize() - one which
accepts function AND Jacobian or one which accepts ONLY function.
Be careful to choose variant of MinNLCOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinNLCOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinNLCOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinNLCCreateF() | works FAILS
MinNLCCreate() | FAILS works
Here "FAILS" denotes inappropriate combinations of optimizer creation
function and MinNLCOptimize() version. Attemps to use such
combination will lead to exception. Either you did not pass gradient
when it WAS needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcoptimize(minnlcstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minnlcoptimize(minnlcstate &state,
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic gradient/Jacobian.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function (constraints) at the
initial point (note: future versions may also perform check at the final
point) and compares numerical gradient/Jacobian with analytic one provided
by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both gradients/Jacobians, and specific components highlighted
as suspicious by the OptGuard.
The primary OptGuard report can be retrieved with minnlcoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with minnlcsetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcoptguardgradient(const minnlcstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates nonsmoothness monitoring option of
the OptGuard integrity checker. Smoothness monitor silently observes
solution process and tries to detect ill-posed problems, i.e. ones with:
a) discontinuous target function (non-C0) and/or constraints
b) nonsmooth target function (non-C1) and/or constraints
Smoothness monitoring does NOT interrupt optimization even if it suspects
that your problem is nonsmooth. It just sets corresponding flags in the
OptGuard report which can be retrieved after optimization is over.
Smoothness monitoring is a moderate overhead option which often adds less
than 1% to the optimizer running time. Thus, you can use it even for large
scale problems.
NOTE: OptGuard does NOT guarantee that it will always detect C0/C1
continuity violations.
First, minor errors are hard to catch - say, a 0.0001 difference in
the model values at two sides of the gap may be due to discontinuity
of the model - or simply because the model has changed.
Second, C1-violations are especially difficult to detect in a
noninvasive way. The optimizer usually performs very short steps
near the nonsmoothness, and differentiation usually introduces a
lot of numerical noise. It is hard to tell whether some tiny
discontinuity in the slope is due to real nonsmoothness or just due
to numerical noise alone.
Our top priority was to avoid false positives, so in some rare cases
minor errors may went unnoticed (however, in most cases they can be
spotted with restart from different initial point).
INPUT PARAMETERS:
state - algorithm state
level - monitoring level:
* 0 - monitoring is disabled
* 1 - noninvasive low-overhead monitoring; function values
and/or gradients are recorded, but OptGuard does not
try to perform additional evaluations in order to
get more information about suspicious locations.
This kind of monitoring does not work well with SQP
because SQP solver needs just 1-2 function evaluations
per step, which is not enough for OptGuard to make
any conclusions.
=== EXPLANATION ==========================================================
One major source of headache during optimization is the possibility of
the coding errors in the target function/constraints (or their gradients).
Such errors most often manifest themselves as discontinuity or
nonsmoothness of the target/constraints.
Another frequent situation is when you try to optimize something involving
lots of min() and max() operations, i.e. nonsmooth target. Although not a
coding error, it is nonsmoothness anyway - and smooth optimizers usually
stop right after encountering nonsmoothness, well before reaching solution.
OptGuard integrity checker helps you to catch such situations: it monitors
function values/gradients being passed to the optimizer and tries to
errors. Upon discovering suspicious pair of points it raises appropriate
flag (and allows you to continue optimization). When optimization is done,
you can study OptGuard result.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minnlcoptguardsmoothness(const minnlcstate &state, const ae_int_t level, const xparams _xparams = alglib::xdefault);
void minnlcoptguardsmoothness(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
=== PRIMARY REPORT =======================================================
OptGuard performs several checks which are intended to catch common errors
in the implementation of nonlinear function/gradient:
* incorrect analytic gradient
* discontinuous (non-C0) target functions (constraints)
* nonsmooth (non-C1) target functions (constraints)
Each of these checks is activated with appropriate function:
* minnlcoptguardgradient() for gradient verification
* minnlcoptguardsmoothness() for C0/C1 checks
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradfidx for specific function (Jacobian row) suspected
* rep.badgradvidx for specific variable (Jacobian column) suspected
* rep.badgradxbase, a point where gradient/Jacobian is tested
* rep.badgraduser, user-provided gradient/Jacobian
* rep.badgradnum, reference gradient/Jacobian obtained via numerical
differentiation
* rep.nonc0suspected, and additionally:
* rep.nonc0fidx - an index of specific function violating C0 continuity
* rep.nonc1suspected, and additionally
* rep.nonc1fidx - an index of specific function violating C1 continuity
Here function index 0 means target function, index 1 or higher denotes
nonlinear constraints.
=== ADDITIONAL REPORTS/LOGS ==============================================
Several different tests are performed to catch C0/C1 errors, you can find
out specific test signaled error by looking to:
* rep.nonc0test0positive, for non-C0 test #0
* rep.nonc1test0positive, for non-C1 test #0
* rep.nonc1test1positive, for non-C1 test #1
Additional information (including line search logs) can be obtained by
means of:
* minnlcoptguardnonc1test0results()
* minnlcoptguardnonc1test1results()
which return detailed error reports, specific points where discontinuities
were found, and so on.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - generic OptGuard report; more detailed reports can be
retrieved with other functions.
NOTE: false negatives (nonsmooth problems are not identified as nonsmooth
ones) are possible although unlikely.
The reason is that you need to make several evaluations around
nonsmoothness in order to accumulate enough information about
function curvature. Say, if you start right from the nonsmooth point,
optimizer simply won't get enough data to understand what is going
wrong before it terminates due to abrupt changes in the derivative.
It is also possible that "unlucky" step will move us to the
termination too quickly.
Our current approach is to have less than 0.1% false negatives in
our test examples (measured with multiple restarts from random
points), and to have exactly 0% false positives.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minnlcoptguardresults(const minnlcstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #0
Nonsmoothness (non-C1) test #0 studies function values (not gradient!)
obtained during line searches and monitors behavior of the directional
derivative estimate.
This test is less powerful than test #1, but it does not depend on the
gradient values and thus it is more robust against artifacts introduced by
numerical differentiation.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* fidx - is an index of the function (0 for target function, 1 or higher
for nonlinear constraints) which is suspected of being "non-C1"
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #0 "strong" report
lngrep - C1 test #0 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minnlcoptguardnonc1test0results(const minnlcstate &state, optguardnonc1test0report &strrep, optguardnonc1test0report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #1
Nonsmoothness (non-C1) test #1 studies individual components of the
gradient computed during line search.
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* fidx - is an index of the function (0 for target function, 1 or higher
for nonlinear constraints) which is suspected of being "non-C1"
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #1 "strong" report
lngrep - C1 test #1 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minnlcoptguardnonc1test1results(const minnlcstate &state, optguardnonc1test1report &strrep, optguardnonc1test1report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
MinNLC results: the solution found, completion codes and additional
information.
If you activated OptGuard integrity checking functionality and want to get
OptGuard report, it can be retrieved with:
* minnlcoptguardresults() - for a primary report about (a) suspected C0/C1
continuity violations and (b) errors in the analytic gradient.
* minnlcoptguardnonc1test0results() - for C1 continuity violation test #0,
detailed line search log
* minnlcoptguardnonc1test1results() - for C1 continuity violation test #1,
detailed line search log
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report, contains information about completion
code, constraint violation at the solution and so on.
You should check rep.terminationtype in order to
distinguish successful termination from unsuccessful one:
=== FAILURE CODES ===
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -3 box constraints are infeasible.
Note: infeasibility of non-box constraints does
NOT trigger emergency completion; you have
to examine rep.bcerr/rep.lcerr/rep.nlcerr to
detect possibly inconsistent constraints.
=== SUCCESS CODES ===
* 2 scaled step is no more than EpsX.
* 5 MaxIts steps were taken.
* 8 user requested algorithm termination via
minnlcrequesttermination(), last accepted point is
returned.
More information about fields of this structure can be
found in the comments on minnlcreport datatype.
-- ALGLIB --
Copyright 06.06.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcresults(const minnlcstate &state, real_1d_array &x, minnlcreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
NLC results
Buffered implementation of MinNLCResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcresultsbuf(const minnlcstate &state, real_1d_array &x, minnlcreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minnlcrequesttermination(const minnlcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with MinNLCCreate call.
X - new starting point.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnlcrestartfrom(const minnlcstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MINBC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
BOX CONSTRAINED OPTIMIZATION
WITH FAST ACTIVATION OF MULTIPLE BOX CONSTRAINTS
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to box
constraints (with some of box constraints actually being equality ones).
This optimizer uses algorithm similar to that of MinBLEIC (optimizer with
general linear constraints), but presence of box-only constraints allows
us to use faster constraint activation strategies. On large-scale problems,
with multiple constraints active at the solution, this optimizer can be
several times faster than BLEIC.
REQUIREMENTS:
* user must provide function value and gradient
* starting point X0 must be feasible or
not too far away from the feasible set
* grad(f) must be Lipschitz continuous on a level set:
L = { x : f(x)<=f(x0) }
* function must be defined everywhere on the feasible set F
USAGE:
Constrained optimization if far more complex than the unconstrained one.
Here we give very brief outline of the BC optimizer. We strongly recommend
you to read examples in the ALGLIB Reference Manual and to read ALGLIB User Guide
on optimization, which is available at http://www.alglib.net/optimization/
1. User initializes algorithm state with MinBCCreate() call
2. USer adds box constraints by calling MinBCSetBC() function.
3. User sets stopping conditions with MinBCSetCond().
4. User calls MinBCOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
5. User calls MinBCResults() to get solution
6. Optionally user may call MinBCRestartFrom() to solve another problem
with same N but another starting point.
MinBCRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size ofX
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbccreate(const ae_int_t n, const real_1d_array &x, minbcstate &state, const xparams _xparams = alglib::xdefault);
void minbccreate(const real_1d_array &x, minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
The subroutine is finite difference variant of MinBCCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinBCCreate() in order to get
more information about creation of BC optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinBCSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. CG needs exact gradient values. Imprecise
gradient may slow down convergence, especially on highly nonlinear
problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void minbccreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minbcstate &state, const xparams _xparams = alglib::xdefault);
void minbccreatef(const real_1d_array &x, const double diffstep, minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets boundary constraints for BC optimizer.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with MinBCRestartFrom().
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: this solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints,
even when numerical differentiation is used (algorithm adjusts nodes
according to boundary constraints)
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetbc(const minbcstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for the optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinBCSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - step vector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinBCSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0 and EpsX=0 and MaxIts=0 (simultaneously) will lead
to automatic stopping criterion selection.
NOTE: when SetCond() called with non-zero MaxIts, BC solver may perform
slightly more than MaxIts iterations. I.e., MaxIts sets non-strict
limit on iterations count.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetcond(const minbcstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for BC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the BC too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinBCSetPrec...()
functions.
There is a special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minbcsetscale(const minbcstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: preconditioning is turned off.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetprecdefault(const minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE 1: D[i] should be positive. Exception will be thrown otherwise.
NOTE 2: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetprecdiag(const minbcstate &state, const real_1d_array &d, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinBCSetScale()
call (before or after MinBCSetPrecScale() call). Without knowledge of
the scale of your variables scale-based preconditioner will be just unit
matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetprecscale(const minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinBCOptimize().
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetxrep(const minbcstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which lead to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minbcsetstpmax(const minbcstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minbciteration(const minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinBCCreate() for analytical gradient or MinBCCreateF()
for numerical differentiation) you should choose appropriate variant of
MinBCOptimize() - one which accepts function AND gradient or one
which accepts function ONLY.
Be careful to choose variant of MinBCOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinBCOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinBCOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinBCCreateF() | works FAILS
MinBCCreate() | FAILS works
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinBCOptimize() version. Attemps to use such
combination (for example, to create optimizer with MinBCCreateF()
and to pass gradient information to MinCGOptimize()) will lead to
exception being thrown. Either you did not pass gradient when it WAS
needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcoptimize(minbcstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minbcoptimize(minbcstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic gradient.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function at the initial point
(note: future versions may also perform check at the final point) and
compares numerical gradient with analytic one provided by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both gradients and specific components highlighted as
suspicious by the OptGuard.
The primary OptGuard report can be retrieved with minbcoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with minbcsetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minbcoptguardgradient(const minbcstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates nonsmoothness monitoring option of
the OptGuard integrity checker. Smoothness monitor silently observes
solution process and tries to detect ill-posed problems, i.e. ones with:
a) discontinuous target function (non-C0)
b) nonsmooth target function (non-C1)
Smoothness monitoring does NOT interrupt optimization even if it suspects
that your problem is nonsmooth. It just sets corresponding flags in the
OptGuard report which can be retrieved after optimization is over.
Smoothness monitoring is a moderate overhead option which often adds less
than 1% to the optimizer running time. Thus, you can use it even for large
scale problems.
NOTE: OptGuard does NOT guarantee that it will always detect C0/C1
continuity violations.
First, minor errors are hard to catch - say, a 0.0001 difference in
the model values at two sides of the gap may be due to discontinuity
of the model - or simply because the model has changed.
Second, C1-violations are especially difficult to detect in a
noninvasive way. The optimizer usually performs very short steps
near the nonsmoothness, and differentiation usually introduces a
lot of numerical noise. It is hard to tell whether some tiny
discontinuity in the slope is due to real nonsmoothness or just due
to numerical noise alone.
Our top priority was to avoid false positives, so in some rare cases
minor errors may went unnoticed (however, in most cases they can be
spotted with restart from different initial point).
INPUT PARAMETERS:
state - algorithm state
level - monitoring level:
* 0 - monitoring is disabled
* 1 - noninvasive low-overhead monitoring; function values
and/or gradients are recorded, but OptGuard does not
try to perform additional evaluations in order to
get more information about suspicious locations.
=== EXPLANATION ==========================================================
One major source of headache during optimization is the possibility of
the coding errors in the target function/constraints (or their gradients).
Such errors most often manifest themselves as discontinuity or
nonsmoothness of the target/constraints.
Another frequent situation is when you try to optimize something involving
lots of min() and max() operations, i.e. nonsmooth target. Although not a
coding error, it is nonsmoothness anyway - and smooth optimizers usually
stop right after encountering nonsmoothness, well before reaching solution.
OptGuard integrity checker helps you to catch such situations: it monitors
function values/gradients being passed to the optimizer and tries to
errors. Upon discovering suspicious pair of points it raises appropriate
flag (and allows you to continue optimization). When optimization is done,
you can study OptGuard result.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbcoptguardsmoothness(const minbcstate &state, const ae_int_t level, const xparams _xparams = alglib::xdefault);
void minbcoptguardsmoothness(const minbcstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
=== PRIMARY REPORT =======================================================
OptGuard performs several checks which are intended to catch common errors
in the implementation of nonlinear function/gradient:
* incorrect analytic gradient
* discontinuous (non-C0) target functions (constraints)
* nonsmooth (non-C1) target functions (constraints)
Each of these checks is activated with appropriate function:
* minbcoptguardgradient() for gradient verification
* minbcoptguardsmoothness() for C0/C1 checks
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradvidx for specific variable (gradient element) suspected
* rep.badgradxbase, a point where gradient is tested
* rep.badgraduser, user-provided gradient (stored as 2D matrix with
single row in order to make report structure compatible with more
complex optimizers like MinNLC or MinLM)
* rep.badgradnum, reference gradient obtained via numerical
differentiation (stored as 2D matrix with single row in order to make
report structure compatible with more complex optimizers like MinNLC
or MinLM)
* rep.nonc0suspected
* rep.nonc1suspected
=== ADDITIONAL REPORTS/LOGS ==============================================
Several different tests are performed to catch C0/C1 errors, you can find
out specific test signaled error by looking to:
* rep.nonc0test0positive, for non-C0 test #0
* rep.nonc1test0positive, for non-C1 test #0
* rep.nonc1test1positive, for non-C1 test #1
Additional information (including line search logs) can be obtained by
means of:
* minbcoptguardnonc1test0results()
* minbcoptguardnonc1test1results()
which return detailed error reports, specific points where discontinuities
were found, and so on.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - generic OptGuard report; more detailed reports can be
retrieved with other functions.
NOTE: false negatives (nonsmooth problems are not identified as nonsmooth
ones) are possible although unlikely.
The reason is that you need to make several evaluations around
nonsmoothness in order to accumulate enough information about
function curvature. Say, if you start right from the nonsmooth point,
optimizer simply won't get enough data to understand what is going
wrong before it terminates due to abrupt changes in the derivative.
It is also possible that "unlucky" step will move us to the
termination too quickly.
Our current approach is to have less than 0.1% false negatives in
our test examples (measured with multiple restarts from random
points), and to have exactly 0% false positives.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbcoptguardresults(const minbcstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #0
Nonsmoothness (non-C1) test #0 studies function values (not gradient!)
obtained during line searches and monitors behavior of the directional
derivative estimate.
This test is less powerful than test #1, but it does not depend on the
gradient values and thus it is more robust against artifacts introduced by
numerical differentiation.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #0 "strong" report
lngrep - C1 test #0 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbcoptguardnonc1test0results(const minbcstate &state, optguardnonc1test0report &strrep, optguardnonc1test0report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #1
Nonsmoothness (non-C1) test #1 studies individual components of the
gradient computed during line search.
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #1 "strong" report
lngrep - C1 test #1 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minbcoptguardnonc1test1results(const minbcstate &state, optguardnonc1test1report &strrep, optguardnonc1test1report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
BC results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -3 inconsistent constraints.
* 1 relative function improvement is no more than EpsF.
* 2 scaled step is no more than EpsX.
* 4 scaled gradient norm is no more than EpsG.
* 5 MaxIts steps was taken
* 8 terminated by user who called minbcrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
More information about fields of this structure can be
found in the comments on MinBCReport datatype.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcresults(const minbcstate &state, real_1d_array &x, minbcreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
BC results
Buffered implementation of MinBCResults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcresultsbuf(const minbcstate &state, real_1d_array &x, minbcreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with MinBCCreate call.
X - new starting point.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbcrestartfrom(const minbcstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minbcrequesttermination(const minbcstate &state, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MINNS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
NONSMOOTH NONCONVEX OPTIMIZATION
SUBJECT TO BOX/LINEAR/NONLINEAR-NONSMOOTH CONSTRAINTS
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments subject to any
combination of:
* bound constraints
* linear inequality constraints
* linear equality constraints
* nonlinear equality constraints Gi(x)=0
* nonlinear inequality constraints Hi(x)<=0
IMPORTANT: see MinNSSetAlgoAGS for important information on performance
restrictions of AGS solver.
REQUIREMENTS:
* starting point X0 must be feasible or not too far away from the feasible
set
* F(), G(), H() are continuous, locally Lipschitz and continuously (but
not necessarily twice) differentiable in an open dense subset of R^N.
Functions F(), G() and H() may be nonsmooth and non-convex.
Informally speaking, it means that functions are composed of large
differentiable "patches" with nonsmoothness having place only at the
boundaries between these "patches".
Most real-life nonsmooth functions satisfy these requirements. Say,
anything which involves finite number of abs(), min() and max() is very
likely to pass the test.
Say, it is possible to optimize anything of the following:
* f=abs(x0)+2*abs(x1)
* f=max(x0,x1)
* f=sin(max(x0,x1)+abs(x2))
* for nonlinearly constrained problems: F() must be bounded from below
without nonlinear constraints (this requirement is due to the fact that,
contrary to box and linear constraints, nonlinear ones require special
handling).
* user must provide function value and gradient for F(), H(), G() at all
points where function/gradient can be calculated. If optimizer requires
value exactly at the boundary between "patches" (say, at x=0 for f=abs(x)),
where gradient is not defined, user may resolve tie arbitrarily (in our
case - return +1 or -1 at its discretion).
* NS solver supports numerical differentiation, i.e. it may differentiate
your function for you, but it results in 2N increase of function
evaluations. Not recommended unless you solve really small problems. See
minnscreatef() for more information on this functionality.
USAGE:
1. User initializes algorithm state with MinNSCreate() call and chooses
what NLC solver to use. There is some solver which is used by default,
with default settings, but you should NOT rely on default choice. It
may change in future releases of ALGLIB without notice, and no one can
guarantee that new solver will be able to solve your problem with
default settings.
From the other side, if you choose solver explicitly, you can be pretty
sure that it will work with new ALGLIB releases.
In the current release following solvers can be used:
* AGS solver (activated with MinNSSetAlgoAGS() function)
2. User adds boundary and/or linear and/or nonlinear constraints by means
of calling one of the following functions:
a) MinNSSetBC() for boundary constraints
b) MinNSSetLC() for linear constraints
c) MinNSSetNLC() for nonlinear constraints
You may combine (a), (b) and (c) in one optimization problem.
3. User sets scale of the variables with MinNSSetScale() function. It is
VERY important to set scale of the variables, because nonlinearly
constrained problems are hard to solve when variables are badly scaled.
4. User sets stopping conditions with MinNSSetCond().
5. Finally, user calls MinNSOptimize() function which takes algorithm
state and pointer (delegate, etc) to callback function which calculates
F/G/H.
7. User calls MinNSResults() to get solution
8. Optionally user may call MinNSRestartFrom() to solve another problem
with same N but another starting point. MinNSRestartFrom() allows to
reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
OUTPUT PARAMETERS:
State - structure stores algorithm state
NOTE: minnscreatef() function may be used if you do not have analytic
gradient. This function creates solver which uses numerical
differentiation with user-specified step.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnscreate(const ae_int_t n, const real_1d_array &x, minnsstate &state, const xparams _xparams = alglib::xdefault);
void minnscreate(const real_1d_array &x, minnsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Version of minnscreatef() which uses numerical differentiation. I.e., you
do not have to calculate derivatives yourself. However, this version needs
2N times more function evaluations.
2-point differentiation formula is used, because more precise 4-point
formula is unstable when used on non-smooth functions.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[N]:
* it is better to set X to a feasible point
* but X can be infeasible, in which case algorithm will try
to find feasible point first, using X as initial
approximation.
DiffStep- differentiation step, DiffStep>0. Algorithm performs
numerical differentiation with step for I-th variable
being equal to DiffStep*S[I] (here S[] is a scale vector,
set by minnssetscale() function).
Do not use too small steps, because it may lead to
catastrophic cancellation during intermediate calculations.
OUTPUT PARAMETERS:
State - structure stores algorithm state
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnscreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, minnsstate &state, const xparams _xparams = alglib::xdefault);
void minnscreatef(const real_1d_array &x, const double diffstep, minnsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets boundary constraints.
Boundary constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with minnsrestartfrom().
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF.
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF.
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: AGS solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints,
even when numerical differentiation is used (algorithm adjusts nodes
according to boundary constraints)
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetbc(const minnsstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets linear constraints.
Linear constraints are inactive by default (after initial creation).
They are preserved after algorithm restart with minnsrestartfrom().
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
NOTE: linear (non-bound) constraints are satisfied only approximately:
* there always exists some minor violation (about current sampling radius
in magnitude during optimization, about EpsX in the solution) due to use
of penalty method to handle constraints.
* numerical differentiation, if used, may lead to function evaluations
outside of the feasible area, because algorithm does NOT change
numerical differentiation formula according to linear constraints.
If you want constraints to be satisfied exactly, try to reformulate your
problem in such manner that all constraints will become boundary ones
(this kind of constraints is always satisfied exactly, both in the final
solution and in all intermediate points).
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetlc(const minnsstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minnssetlc(const minnsstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets nonlinear constraints.
In fact, this function sets NUMBER of nonlinear constraints. Constraints
itself (constraint functions) are passed to minnsoptimize() method. This
method requires user-defined vector function F[] and its Jacobian J[],
where:
* first component of F[] and first row of Jacobian J[] correspond to
function being minimized
* next NLEC components of F[] (and rows of J) correspond to nonlinear
equality constraints G_i(x)=0
* next NLIC components of F[] (and rows of J) correspond to nonlinear
inequality constraints H_i(x)<=0
NOTE: you may combine nonlinear constraints with linear/boundary ones. If
your problem has mixed constraints, you may explicitly specify some
of them as linear ones. It may help optimizer to handle them more
efficiently.
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
NLEC - number of Non-Linear Equality Constraints (NLEC), >=0
NLIC - number of Non-Linear Inquality Constraints (NLIC), >=0
NOTE 1: nonlinear constraints are satisfied only approximately! It is
possible that algorithm will evaluate function outside of
the feasible area!
NOTE 2: algorithm scales variables according to scale specified by
minnssetscale() function, so it can handle problems with badly
scaled variables (as long as we KNOW their scales).
However, there is no way to automatically scale nonlinear
constraints Gi(x) and Hi(x). Inappropriate scaling of Gi/Hi may
ruin convergence. Solving problem with constraint "1000*G0(x)=0"
is NOT same as solving it with constraint "0.001*G0(x)=0".
It means that YOU are the one who is responsible for correct
scaling of nonlinear constraints Gi(x) and Hi(x). We recommend you
to scale nonlinear constraints in such way that I-th component of
dG/dX (or dH/dx) has approximately unit magnitude (for problems
with unit scale) or has magnitude approximately equal to 1/S[i]
(where S is a scale set by minnssetscale() function).
NOTE 3: nonlinear constraints are always hard to handle, no matter what
algorithm you try to use. Even basic box/linear constraints modify
function curvature by adding valleys and ridges. However,
nonlinear constraints add valleys which are very hard to follow
due to their "curved" nature.
It means that optimization with single nonlinear constraint may be
significantly slower than optimization with multiple linear ones.
It is normal situation, and we recommend you to carefully choose
Rho parameter of minnssetalgoags(), because too large value may
slow down convergence.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetnlc(const minnsstate &state, const ae_int_t nlec, const ae_int_t nlic, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for iterations of optimizer.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The AGS solver finishes its work if on k+1-th iteration
sampling radius decreases below EpsX.
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
stopping criterion selection. We do not recommend you to rely on default
choice in production code.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetcond(const minnsstate &state, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for NLC optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of the optimizer - step
along I-th axis is equal to DiffStep*S[I].
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetscale(const minnsstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function tells MinNS unit to use AGS (adaptive gradient sampling)
algorithm for nonsmooth constrained optimization. This algorithm is a
slight modification of one described in "An Adaptive Gradient Sampling
Algorithm for Nonsmooth Optimization" by Frank E. Curtisy and Xiaocun Quez.
This optimizer has following benefits and drawbacks:
+ robustness; it can be used with nonsmooth and nonconvex functions.
+ relatively easy tuning; most of the metaparameters are easy to select.
- it has convergence of steepest descent, slower than CG/LBFGS.
- each iteration involves evaluation of ~2N gradient values and solution
of 2Nx2N quadratic programming problem, which limits applicability of
algorithm by small-scale problems (up to 50-100).
IMPORTANT: this algorithm has convergence guarantees, i.e. it will
steadily move towards some stationary point of the function.
However, "stationary point" does not always mean "solution".
Nonsmooth problems often have "flat spots", i.e. areas where
function do not change at all. Such "flat spots" are stationary
points by definition, and algorithm may be caught here.
Nonsmooth CONVEX tasks are not prone to this problem. Say, if
your function has form f()=MAX(f0,f1,...), and f_i are convex,
then f() is convex too and you have guaranteed convergence to
solution.
INPUT PARAMETERS:
State - structure which stores algorithm state
Radius - initial sampling radius, >=0.
Internally multiplied by vector of per-variable scales
specified by minnssetscale()).
You should select relatively large sampling radius, roughly
proportional to scaled length of the first steps of the
algorithm. Something close to 0.1 in magnitude should be
good for most problems.
AGS solver can automatically decrease radius, so too large
radius is not a problem (assuming that you won't choose
so large radius that algorithm will sample function in
too far away points, where gradient value is irrelevant).
Too small radius won't cause algorithm to fail, but it may
slow down algorithm (it may have to perform too short
steps).
Penalty - penalty coefficient for nonlinear constraints:
* for problem with nonlinear constraints should be some
problem-specific positive value, large enough that
penalty term changes shape of the function.
Starting from some problem-specific value penalty
coefficient becomes large enough to exactly enforce
nonlinear constraints; larger values do not improve
precision.
Increasing it too much may slow down convergence, so you
should choose it carefully.
* can be zero for problems WITHOUT nonlinear constraints
(i.e. for unconstrained ones or ones with just box or
linear constraints)
* if you specify zero value for problem with at least one
nonlinear constraint, algorithm will terminate with
error code -1.
ALGORITHM OUTLINE
The very basic outline of unconstrained AGS algorithm is given below:
0. If sampling radius is below EpsX or we performed more then MaxIts
iterations - STOP.
1. sample O(N) gradient values at random locations around current point;
informally speaking, this sample is an implicit piecewise linear model
of the function, although algorithm formulation does not mention that
explicitly
2. solve quadratic programming problem in order to find descent direction
3. if QP solver tells us that we are near solution, decrease sampling
radius and move to (0)
4. perform backtracking line search
5. after moving to new point, goto (0)
As for the constraints:
* box constraints are handled exactly by modification of the function
being minimized
* linear/nonlinear constraints are handled by adding L1 penalty. Because
our solver can handle nonsmoothness, we can use L1 penalty function,
which is an exact one (i.e. exact solution is returned under such
penalty).
* penalty coefficient for linear constraints is chosen automatically;
however, penalty coefficient for nonlinear constraints must be specified
by user.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnssetalgoags(const minnsstate &state, const double radius, const double penalty, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to minnsoptimize().
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minnssetxrep(const minnsstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsrequesttermination(const minnsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minnsiteration(const minnsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied Jacobian, and one which uses only function
vector and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
you should choose appropriate variant of minnsoptimize() - one which
accepts function AND Jacobian or one which accepts ONLY function.
Be careful to choose variant of minnsoptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to minnsoptimize() and specific
function used to create optimizer.
| USER PASSED TO minnsoptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
minnscreatef() | works FAILS
minnscreate() | FAILS works
Here "FAILS" denotes inappropriate combinations of optimizer creation
function and minnsoptimize() version. Attemps to use such
combination will lead to exception. Either you did not pass gradient
when it WAS needed or you passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsoptimize(minnsstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minnsoptimize(minnsstate &state,
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
MinNS results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report. You should check Rep.TerminationType
in order to distinguish successful termination from
unsuccessful one:
* -8 internal integrity control detected infinite or
NAN values in function/gradient. Abnormal
termination signalled.
* -3 box constraints are inconsistent
* -1 inconsistent parameters were passed:
* penalty parameter for minnssetalgoags() is zero,
but we have nonlinear constraints set by minnssetnlc()
* 2 sampling radius decreased below epsx
* 7 stopping conditions are too stringent,
further improvement is impossible,
X contains best point found so far.
* 8 User requested termination via minnsrequesttermination()
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsresults(const minnsstate &state, real_1d_array &x, minnsreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Buffered implementation of minnsresults() which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsresultsbuf(const minnsstate &state, real_1d_array &x, minnsreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts algorithm from new point.
All optimization parameters (including constraints) are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure previously allocated with minnscreate() call.
X - new starting point.
-- ALGLIB --
Copyright 18.05.2015 by Bochkanov Sergey
*************************************************************************/
void minnsrestartfrom(const minnsstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MINCOMP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Obsolete function, use MinLBFGSSetPrecDefault() instead.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetdefaultpreconditioner(const minlbfgsstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete function, use MinLBFGSSetCholeskyPreconditioner() instead.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetcholeskypreconditioner(const minlbfgsstate &state, const real_2d_array &p, const bool isupper, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This is obsolete function which was used by previous version of the BLEIC
optimizer. It does nothing in the current version of BLEIC.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbarrierwidth(const minbleicstate &state, const double mu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This is obsolete function which was used by previous version of the BLEIC
optimizer. It does nothing in the current version of BLEIC.
-- ALGLIB --
Copyright 28.11.2010 by Bochkanov Sergey
*************************************************************************/
void minbleicsetbarrierdecay(const minbleicstate &state, const double mudecay, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
void minasacreate(const ae_int_t n, const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, minasastate &state, const xparams _xparams = alglib::xdefault);
void minasacreate(const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, minasastate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetcond(const minasastate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetxrep(const minasastate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetalgorithm(const minasastate &state, const ae_int_t algotype, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetstpmax(const minasastate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minasaiteration(const minasastate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaoptimize(minasastate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaresults(const minasastate &state, real_1d_array &x, minasareport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
void minasaresultsbuf(const minasastate &state, real_1d_array &x, minasareport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minasarestartfrom(const minasastate &state, const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MINCG) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
NONLINEAR CONJUGATE GRADIENT METHOD
DESCRIPTION:
The subroutine minimizes function F(x) of N arguments by using one of the
nonlinear conjugate gradient methods.
These CG methods are globally convergent (even on non-convex functions) as
long as grad(f) is Lipschitz continuous in a some neighborhood of the
L = { x : f(x)<=f(x0) }.
REQUIREMENTS:
Algorithm will request following information during its operation:
* function value F and its gradient G (simultaneously) at given point X
USAGE:
1. User initializes algorithm state with MinCGCreate() call
2. User tunes solver parameters with MinCGSetCond(), MinCGSetStpMax() and
other functions
3. User calls MinCGOptimize() function which takes algorithm state and
pointer (delegate, etc.) to callback function which calculates F/G.
4. User calls MinCGResults() to get solution
5. Optionally, user may call MinCGRestartFrom() to solve another problem
with same N but another starting point and/or another function.
MinCGRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 25.03.2010 by Bochkanov Sergey
*************************************************************************/
void mincgcreate(const ae_int_t n, const real_1d_array &x, mincgstate &state, const xparams _xparams = alglib::xdefault);
void mincgcreate(const real_1d_array &x, mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
The subroutine is finite difference variant of MinCGCreate(). It uses
finite differences in order to differentiate target function.
Description below contains information which is specific to this function
only. We recommend to read comments on MinCGCreate() in order to get more
information about creation of CG optimizer.
INPUT PARAMETERS:
N - problem dimension, N>0:
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - starting point, array[0..N-1].
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. algorithm uses 4-point central formula for differentiation.
2. differentiation step along I-th axis is equal to DiffStep*S[I] where
S[] is scaling vector which can be set by MinCGSetScale() call.
3. we recommend you to use moderate values of differentiation step. Too
large step will result in too large truncation errors, while too small
step will result in too large numerical errors. 1.0E-6 can be good
value to start with.
4. Numerical differentiation is very inefficient - one gradient
calculation needs 4*N function evaluations. This function will work for
any N - either small (1...10), moderate (10...100) or large (100...).
However, performance penalty will be too severe for any N's except for
small ones.
We should also say that code which relies on numerical differentiation
is less robust and precise. L-BFGS needs exact gradient values.
Imprecise gradient may slow down convergence, especially on highly
nonlinear problems.
Thus we recommend to use this function for fast prototyping on small-
dimensional problems only, and to implement analytical gradient as soon
as possible.
-- ALGLIB --
Copyright 16.05.2011 by Bochkanov Sergey
*************************************************************************/
void mincgcreatef(const ae_int_t n, const real_1d_array &x, const double diffstep, mincgstate &state, const xparams _xparams = alglib::xdefault);
void mincgcreatef(const real_1d_array &x, const double diffstep, mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for CG optimization algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsG - >=0
The subroutine finishes its work if the condition
|v|<EpsG is satisfied, where:
* |.| means Euclidian norm
* v - scaled gradient vector, v[i]=g[i]*s[i]
* g - gradient
* s - scaling coefficients set by MinCGSetScale()
EpsF - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |F(k+1)-F(k)|<=EpsF*max{|F(k)|,|F(k+1)|,1}
is satisfied.
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinCGSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited.
Passing EpsG=0, EpsF=0, EpsX=0 and MaxIts=0 (simultaneously) will lead to
automatic stopping criterion selection (small EpsX).
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetcond(const mincgstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for CG optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Scaling is also used by finite difference variant of CG optimizer - step
along I-th axis is equal to DiffStep*S[I].
In most optimizers (and in the CG too) scaling is NOT a form of
preconditioning. It just affects stopping conditions. You should set
preconditioner by separate call to one of the MinCGSetPrec...() functions.
There is special preconditioning mode, however, which uses scaling
coefficients to form diagonal preconditioning matrix. You can turn this
mode on, if you want. But you should understand that scaling is not the
same thing as preconditioning - these are two different, although related
forms of tuning solver.
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void mincgsetscale(const mincgstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinCGOptimize().
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetxrep(const mincgstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets CG algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
CGType - algorithm type:
* -1 automatic selection of the best algorithm
* 0 DY (Dai and Yuan) algorithm
* 1 Hybrid DY-HS algorithm
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetcgtype(const mincgstate &state, const ae_int_t cgtype, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetstpmax(const mincgstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function allows to suggest initial step length to the CG algorithm.
Suggested step length is used as starting point for the line search. It
can be useful when you have badly scaled problem, i.e. when ||grad||
(which is used as initial estimate for the first step) is many orders of
magnitude different from the desired step.
Line search may fail on such problems without good estimate of initial
step length. Imagine, for example, problem with ||grad||=10^50 and desired
step equal to 0.1 Line search function will use 10^50 as initial step,
then it will decrease step length by 2 (up to 20 attempts) and will get
10^44, which is still too large.
This function allows us to tell than line search should be started from
some moderate step length, like 1.0, so algorithm will be able to detect
desired step length in a several searches.
Default behavior (when no step is suggested) is to use preconditioner, if
it is available, to generate initial estimate of step length.
This function influences only first iteration of algorithm. It should be
called between MinCGCreate/MinCGRestartFrom() call and MinCGOptimize call.
Suggested step is ignored if you have preconditioner.
INPUT PARAMETERS:
State - structure used to store algorithm state.
Stp - initial estimate of the step length.
Can be zero (no estimate).
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsuggeststep(const mincgstate &state, const double stp, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: preconditioning is turned off.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecdefault(const mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: diagonal of approximate Hessian is
used.
INPUT PARAMETERS:
State - structure which stores algorithm state
D - diagonal of the approximate Hessian, array[0..N-1],
(if larger, only leading N elements are used).
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
NOTE 2: D[i] should be positive. Exception will be thrown otherwise.
NOTE 3: you should pass diagonal of approximate Hessian - NOT ITS INVERSE.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecdiag(const mincgstate &state, const real_1d_array &d, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Modification of the preconditioner: scale-based diagonal preconditioning.
This preconditioning mode can be useful when you don't have approximate
diagonal of Hessian, but you know that your variables are badly scaled
(for example, one variable is in [1,10], and another in [1000,100000]),
and most part of the ill-conditioning comes from different scales of vars.
In this case simple scale-based preconditioner, with H[i] = 1/(s[i]^2),
can greatly improve convergence.
IMPRTANT: you should set scale of your variables with MinCGSetScale() call
(before or after MinCGSetPrecScale() call). Without knowledge of the scale
of your variables scale-based preconditioner will be just unit matrix.
INPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: you can change preconditioner "on the fly", during algorithm
iterations.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void mincgsetprecscale(const mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool mincgiteration(const mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. This function has two different implementations: one which uses exact
(analytical) user-supplied gradient, and one which uses function value
only and numerically differentiates function in order to obtain
gradient.
Depending on the specific function used to create optimizer object
(either MinCGCreate() for analytical gradient or MinCGCreateF() for
numerical differentiation) you should choose appropriate variant of
MinCGOptimize() - one which accepts function AND gradient or one which
accepts function ONLY.
Be careful to choose variant of MinCGOptimize() which corresponds to
your optimization scheme! Table below lists different combinations of
callback (function/gradient) passed to MinCGOptimize() and specific
function used to create optimizer.
| USER PASSED TO MinCGOptimize()
CREATED WITH | function only | function and gradient
------------------------------------------------------------
MinCGCreateF() | work FAIL
MinCGCreate() | FAIL work
Here "FAIL" denotes inappropriate combinations of optimizer creation
function and MinCGOptimize() version. Attemps to use such combination
(for example, to create optimizer with MinCGCreateF() and to pass
gradient information to MinCGOptimize()) will lead to exception being
thrown. Either you did not pass gradient when it WAS needed or you
passed gradient when it was NOT needed.
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgoptimize(mincgstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void mincgoptimize(mincgstate &state,
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic gradient.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function at the initial point
(note: future versions may also perform check at the final point) and
compares numerical gradient with analytic one provided by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both gradients and specific components highlighted as
suspicious by the OptGuard.
The primary OptGuard report can be retrieved with mincgoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with mincgsetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void mincgoptguardgradient(const mincgstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates nonsmoothness monitoring option of
the OptGuard integrity checker. Smoothness monitor silently observes
solution process and tries to detect ill-posed problems, i.e. ones with:
a) discontinuous target function (non-C0)
b) nonsmooth target function (non-C1)
Smoothness monitoring does NOT interrupt optimization even if it suspects
that your problem is nonsmooth. It just sets corresponding flags in the
OptGuard report which can be retrieved after optimization is over.
Smoothness monitoring is a moderate overhead option which often adds less
than 1% to the optimizer running time. Thus, you can use it even for large
scale problems.
NOTE: OptGuard does NOT guarantee that it will always detect C0/C1
continuity violations.
First, minor errors are hard to catch - say, a 0.0001 difference in
the model values at two sides of the gap may be due to discontinuity
of the model - or simply because the model has changed.
Second, C1-violations are especially difficult to detect in a
noninvasive way. The optimizer usually performs very short steps
near the nonsmoothness, and differentiation usually introduces a
lot of numerical noise. It is hard to tell whether some tiny
discontinuity in the slope is due to real nonsmoothness or just due
to numerical noise alone.
Our top priority was to avoid false positives, so in some rare cases
minor errors may went unnoticed (however, in most cases they can be
spotted with restart from different initial point).
INPUT PARAMETERS:
state - algorithm state
level - monitoring level:
* 0 - monitoring is disabled
* 1 - noninvasive low-overhead monitoring; function values
and/or gradients are recorded, but OptGuard does not
try to perform additional evaluations in order to
get more information about suspicious locations.
=== EXPLANATION ==========================================================
One major source of headache during optimization is the possibility of
the coding errors in the target function/constraints (or their gradients).
Such errors most often manifest themselves as discontinuity or
nonsmoothness of the target/constraints.
Another frequent situation is when you try to optimize something involving
lots of min() and max() operations, i.e. nonsmooth target. Although not a
coding error, it is nonsmoothness anyway - and smooth optimizers usually
stop right after encountering nonsmoothness, well before reaching solution.
OptGuard integrity checker helps you to catch such situations: it monitors
function values/gradients being passed to the optimizer and tries to
errors. Upon discovering suspicious pair of points it raises appropriate
flag (and allows you to continue optimization). When optimization is done,
you can study OptGuard result.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void mincgoptguardsmoothness(const mincgstate &state, const ae_int_t level, const xparams _xparams = alglib::xdefault);
void mincgoptguardsmoothness(const mincgstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
=== PRIMARY REPORT =======================================================
OptGuard performs several checks which are intended to catch common errors
in the implementation of nonlinear function/gradient:
* incorrect analytic gradient
* discontinuous (non-C0) target functions (constraints)
* nonsmooth (non-C1) target functions (constraints)
Each of these checks is activated with appropriate function:
* mincgoptguardgradient() for gradient verification
* mincgoptguardsmoothness() for C0/C1 checks
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradvidx for specific variable (gradient element) suspected
* rep.badgradxbase, a point where gradient is tested
* rep.badgraduser, user-provided gradient (stored as 2D matrix with
single row in order to make report structure compatible with more
complex optimizers like MinNLC or MinLM)
* rep.badgradnum, reference gradient obtained via numerical
differentiation (stored as 2D matrix with single row in order to make
report structure compatible with more complex optimizers like MinNLC
or MinLM)
* rep.nonc0suspected
* rep.nonc1suspected
=== ADDITIONAL REPORTS/LOGS ==============================================
Several different tests are performed to catch C0/C1 errors, you can find
out specific test signaled error by looking to:
* rep.nonc0test0positive, for non-C0 test #0
* rep.nonc1test0positive, for non-C1 test #0
* rep.nonc1test1positive, for non-C1 test #1
Additional information (including line search logs) can be obtained by
means of:
* mincgoptguardnonc1test0results()
* mincgoptguardnonc1test1results()
which return detailed error reports, specific points where discontinuities
were found, and so on.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - generic OptGuard report; more detailed reports can be
retrieved with other functions.
NOTE: false negatives (nonsmooth problems are not identified as nonsmooth
ones) are possible although unlikely.
The reason is that you need to make several evaluations around
nonsmoothness in order to accumulate enough information about
function curvature. Say, if you start right from the nonsmooth point,
optimizer simply won't get enough data to understand what is going
wrong before it terminates due to abrupt changes in the derivative.
It is also possible that "unlucky" step will move us to the
termination too quickly.
Our current approach is to have less than 0.1% false negatives in
our test examples (measured with multiple restarts from random
points), and to have exactly 0% false positives.
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void mincgoptguardresults(const mincgstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #0
Nonsmoothness (non-C1) test #0 studies function values (not gradient!)
obtained during line searches and monitors behavior of the directional
derivative estimate.
This test is less powerful than test #1, but it does not depend on the
gradient values and thus it is more robust against artifacts introduced by
numerical differentiation.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], f[] - arrays of length CNT which store step lengths and function
values at these points; f[i] is evaluated in x0+stp[i]*d.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #0 "strong" report
lngrep - C1 test #0 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void mincgoptguardnonc1test0results(const mincgstate &state, optguardnonc1test0report &strrep, optguardnonc1test0report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Detailed results of the OptGuard integrity check for nonsmoothness test #1
Nonsmoothness (non-C1) test #1 studies individual components of the
gradient computed during line search.
When precise analytic gradient is provided this test is more powerful than
test #0 which works with function values and ignores user-provided
gradient. However, test #0 becomes more powerful when numerical
differentiation is employed (in such cases test #1 detects higher levels
of numerical noise and becomes too conservative).
This test also tells specific components of the gradient which violate C1
continuity, which makes it more informative than #0, which just tells that
continuity is violated.
Two reports are returned:
* a "strongest" one, corresponding to line search which had highest
value of the nonsmoothness indicator
* a "longest" one, corresponding to line search which had more function
evaluations, and thus is more detailed
In both cases following fields are returned:
* positive - is TRUE when test flagged suspicious point; FALSE if test
did not notice anything (in the latter cases fields below are empty).
* vidx - is an index of the variable in [0,N) with nonsmooth derivative
* x0[], d[] - arrays of length N which store initial point and direction
for line search (d[] can be normalized, but does not have to)
* stp[], g[] - arrays of length CNT which store step lengths and gradient
values at these points; g[i] is evaluated in x0+stp[i]*d and contains
vidx-th component of the gradient.
* stpidxa, stpidxb - we suspect that function violates C1 continuity
between steps #stpidxa and #stpidxb (usually we have stpidxb=stpidxa+3,
with most likely position of the violation between stpidxa+1 and
stpidxa+2.
==========================================================================
= SHORTLY SPEAKING: build a 2D plot of (stp,f) and look at it - you will
= see where C1 continuity is violated.
==========================================================================
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
strrep - C1 test #1 "strong" report
lngrep - C1 test #1 "long" report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void mincgoptguardnonc1test1results(const mincgstate &state, optguardnonc1test1report &strrep, optguardnonc1test1report &lngrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Conjugate gradient results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -8 internal integrity control detected infinite
or NAN values in function/gradient. Abnormal
termination signalled.
* -7 gradient verification failed.
See MinCGSetGradientCheck() for more information.
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient norm is no more than EpsG
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible,
we return best X found so far
* 8 terminated by user
* Rep.IterationsCount contains iterations count
* NFEV countains number of function calculations
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgresults(const mincgstate &state, real_1d_array &x, mincgreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Conjugate gradient results
Buffered implementation of MinCGResults(), which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 20.04.2009 by Bochkanov Sergey
*************************************************************************/
void mincgresultsbuf(const mincgstate &state, real_1d_array &x, mincgreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts CG algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used to store algorithm state.
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void mincgrestartfrom(const mincgstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void mincgrequesttermination(const mincgstate &state, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MINLM) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
IMPROVED LEVENBERG-MARQUARDT METHOD FOR
NON-LINEAR LEAST SQUARES OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of function which is represented as
sum of squares:
F(x) = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])
using value of function vector f[] and Jacobian of f[].
REQUIREMENTS:
This algorithm will request following information during its operation:
* function vector f[] at given point X
* function vector f[] and Jacobian of f[] (simultaneously) at given point
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts fvec() and jac() callbacks.
First one is used to calculate f[] at given point, second one calculates
f[] and Jacobian df[i]/dx[j].
You can try to initialize MinLMState structure with VJ function and then
use incorrect version of MinLMOptimize() (for example, version which
works with general form function and does not provide Jacobian), but it
will lead to exception being thrown after first attempt to calculate
Jacobian.
USAGE:
1. User initializes algorithm state with MinLMCreateVJ() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of functions f[i]
X - initial solution, array[0..N-1]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatevj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatevj(const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
IMPROVED LEVENBERG-MARQUARDT METHOD FOR
NON-LINEAR LEAST SQUARES OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of function which is represented as
sum of squares:
F(x) = f[0]^2(x[0],...,x[n-1]) + ... + f[m-1]^2(x[0],...,x[n-1])
using value of function vector f[] only. Finite differences are used to
calculate Jacobian.
REQUIREMENTS:
This algorithm will request following information during its operation:
* function vector f[] at given point X
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts fvec() callback.
You can try to initialize MinLMState structure with VJ function and then
use incorrect version of MinLMOptimize() (for example, version which
works with general form function and does not accept function vector), but
it will lead to exception being thrown after first attempt to calculate
Jacobian.
USAGE:
1. User initializes algorithm state with MinLMCreateV() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N/M but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
M - number of functions f[i]
X - initial solution, array[0..N-1]
DiffStep- differentiation step, >0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
See also MinLMIteration, MinLMResults.
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatev(const ae_int_t n, const ae_int_t m, const real_1d_array &x, const double diffstep, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatev(const ae_int_t m, const real_1d_array &x, const double diffstep, minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
LEVENBERG-MARQUARDT-LIKE METHOD FOR NON-LINEAR OPTIMIZATION
DESCRIPTION:
This function is used to find minimum of general form (not "sum-of-
-squares") function
F = F(x[0], ..., x[n-1])
using its gradient and Hessian. Levenberg-Marquardt modification with
L-BFGS pre-optimization and internal pre-conditioned L-BFGS optimization
after each Levenberg-Marquardt step is used.
REQUIREMENTS:
This algorithm will request following information during its operation:
* function value F at given point X
* F and gradient G (simultaneously) at given point X
* F, G and Hessian H (simultaneously) at given point X
There are several overloaded versions of MinLMOptimize() function which
correspond to different LM-like optimization algorithms provided by this
unit. You should choose version which accepts func(), grad() and hess()
function pointers. First pointer is used to calculate F at given point,
second one calculates F(x) and grad F(x), third one calculates F(x),
grad F(x), hess F(x).
You can try to initialize MinLMState structure with FGH-function and then
use incorrect version of MinLMOptimize() (for example, version which does
not provide Hessian matrix), but it will lead to exception being thrown
after first attempt to calculate Hessian.
USAGE:
1. User initializes algorithm state with MinLMCreateFGH() call
2. User tunes solver parameters with MinLMSetCond(), MinLMSetStpMax() and
other functions
3. User calls MinLMOptimize() function which takes algorithm state and
pointers (delegates, etc.) to callback functions.
4. User calls MinLMResults() to get solution
5. Optionally, user may call MinLMRestartFrom() to solve another problem
with same N but another starting point and/or another function.
MinLMRestartFrom() allows to reuse already initialized structure.
INPUT PARAMETERS:
N - dimension, N>1
* if given, only leading N elements of X are used
* if not given, automatically determined from size of X
X - initial solution, array[0..N-1]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
1. you may tune stopping conditions with MinLMSetCond() function
2. if target function contains exp() or other fast growing functions, and
optimization algorithm makes too large steps which leads to overflow,
use MinLMSetStpMax() function to bound algorithm's steps.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefgh(const ae_int_t n, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatefgh(const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets stopping conditions for Levenberg-Marquardt optimization
algorithm.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by MinLMSetScale()
Recommended values: 1E-9 ... 1E-12.
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. Only Levenberg-Marquardt
iterations are counted (L-BFGS/CG iterations are NOT
counted because their cost is very low compared to that of
LM).
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
stopping criterion selection (small EpsX).
NOTE: it is not recommended to set large EpsX (say, 0.001). Because LM is
a second-order method, it performs very precise steps anyway.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetcond(const minlmstate &state, const double epsx, const ae_int_t maxits, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
If NeedXRep is True, algorithm will call rep() callback function if it is
provided to MinLMOptimize(). Both Levenberg-Marquardt and internal L-BFGS
iterations are reported.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetxrep(const minlmstate &state, const bool needxrep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
NOTE: non-zero StpMax leads to moderate performance degradation because
intermediate step of preconditioned L-BFGS optimization is incompatible
with limits on step size.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetstpmax(const minlmstate &state, const double stpmax, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets scaling coefficients for LM optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Generally, scale is NOT considered to be a form of preconditioner. But LM
optimizer is unique in that it uses scaling matrix both in the stopping
condition tests and as Marquardt damping factor.
Proper scaling is very important for the algorithm performance. It is less
important for the quality of results, but still has some influence (it is
easier to converge when variables are properly scaled, so premature
stopping is possible when very badly scalled variables are combined with
relaxed stopping conditions).
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlmsetscale(const minlmstate &state, const real_1d_array &s, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets boundary constraints for LM optimizer
Boundary constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetBC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[N].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[N].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: this solver has following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints
or at its boundary
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlmsetbc(const minlmstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function sets general linear constraints for LM optimizer
Linear constraints are inactive by default (after initial creation). They
are preserved until explicitly turned off with another minlmsetlc() call.
INPUT PARAMETERS:
State - structure stores algorithm state
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
IMPORTANT: if you have linear constraints, it is strongly recommended to
set scale of variables with minlmsetscale(). QP solver which is
used to calculate linearly constrained steps heavily relies on
good scaling of input problems.
IMPORTANT: solvers created with minlmcreatefgh() do not support linear
constraints.
NOTE: linear (non-bound) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations.
NOTE: general linear constraints add significant overhead to solution
process. Although solver performs roughly same amount of iterations
(when compared with similar box-only constrained problem), each
iteration now involves solution of linearly constrained QP
subproblem, which requires ~3-5 times more Cholesky decompositions.
Thus, if you can reformulate your problem in such way this it has
only box constraints, it may be beneficial to do so.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void minlmsetlc(const minlmstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams = alglib::xdefault);
void minlmsetlc(const minlmstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function is used to change acceleration settings
You can choose between three acceleration strategies:
* AccType=0, no acceleration.
* AccType=1, secant updates are used to update quadratic model after each
iteration. After fixed number of iterations (or after model breakdown)
we recalculate quadratic model using analytic Jacobian or finite
differences. Number of secant-based iterations depends on optimization
settings: about 3 iterations - when we have analytic Jacobian, up to 2*N
iterations - when we use finite differences to calculate Jacobian.
AccType=1 is recommended when Jacobian calculation cost is prohibitively
high (several Mx1 function vector calculations followed by several NxN
Cholesky factorizations are faster than calculation of one M*N Jacobian).
It should also be used when we have no Jacobian, because finite difference
approximation takes too much time to compute.
Table below list optimization protocols (XYZ protocol corresponds to
MinLMCreateXYZ) and acceleration types they support (and use by default).
ACCELERATION TYPES SUPPORTED BY OPTIMIZATION PROTOCOLS:
protocol 0 1 comment
V + +
VJ + +
FGH +
DEFAULT VALUES:
protocol 0 1 comment
V x without acceleration it is so slooooooooow
VJ x
FGH x
NOTE: this function should be called before optimization. Attempt to call
it during algorithm iterations may result in unexpected behavior.
NOTE: attempt to call this function with unsupported protocol/acceleration
combination will result in exception being thrown.
-- ALGLIB --
Copyright 14.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlmsetacctype(const minlmstate &state, const ae_int_t acctype, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool minlmiteration(const minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear optimizer
These functions accept following parameters:
state - algorithm state
func - callback which calculates function (or merit function)
value func at given point x
grad - callback which calculates function (or merit function)
value func and gradient grad at given point x
hess - callback which calculates function (or merit function)
value func, gradient grad and Hessian hess at given point x
fvec - callback which calculates function vector fi[]
at given point x
jac - callback which calculates function vector fi[]
and Jacobian jac at given point x
rep - optional callback which is called after each iteration
can be NULL
ptr - optional pointer which is passed to func/grad/hess/jac/rep
can be NULL
NOTES:
1. Depending on function used to create state structure, this algorithm
may accept Jacobian and/or Hessian and/or gradient. According to the
said above, there ase several versions of this function, which accept
different sets of callbacks.
This flexibility opens way to subtle errors - you may create state with
MinLMCreateFGH() (optimization using Hessian), but call function which
does not accept Hessian. So when algorithm will request Hessian, there
will be no callback to call. In this case exception will be thrown.
Be careful to avoid such errors because there is no way to find them at
compile time - you can see them at runtime only.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmoptimize(minlmstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minlmoptimize(minlmstate &state,
void (*fvec)(const real_1d_array &x, real_1d_array &fi, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*hess)(const real_1d_array &x, double &func, real_1d_array &grad, real_2d_array &hess, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
void minlmoptimize(minlmstate &state,
void (*func)(const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr),
void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL,
void *ptr = NULL,
const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function activates/deactivates verification of the user-supplied
analytic Jacobian.
Upon activation of this option OptGuard integrity checker performs
numerical differentiation of your target function vector at the initial
point (note: future versions may also perform check at the final point)
and compares numerical Jacobian with analytic one provided by you.
If difference is too large, an error flag is set and optimization session
continues. After optimization session is over, you can retrieve the report
which stores both Jacobians, and specific components highlighted as
suspicious by the OptGuard.
The OptGuard report can be retrieved with minlmoptguardresults().
IMPORTANT: gradient check is a high-overhead option which will cost you
about 3*N additional function evaluations. In many cases it may
cost as much as the rest of the optimization session.
YOU SHOULD NOT USE IT IN THE PRODUCTION CODE UNLESS YOU WANT TO
CHECK DERIVATIVES PROVIDED BY SOME THIRD PARTY.
NOTE: unlike previous incarnation of the gradient checking code, OptGuard
does NOT interrupt optimization even if it discovers bad gradient.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step used for numerical differentiation:
* TestStep=0 turns verification off
* TestStep>0 activates verification
You should carefully choose TestStep. Value which is
too large (so large that function behavior is non-
cubic at this scale) will lead to false alarms. Too
short step will result in rounding errors dominating
numerical derivative.
You may use different step for different parameters by
means of setting scale with minlmsetscale().
=== EXPLANATION ==========================================================
In order to verify gradient algorithm performs following steps:
* two trial steps are made to X[i]-TestStep*S[i] and X[i]+TestStep*S[i],
where X[i] is i-th component of the initial point and S[i] is a scale
of i-th parameter
* F(X) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
-- ALGLIB --
Copyright 15.06.2014 by Bochkanov Sergey
*************************************************************************/
void minlmoptguardgradient(const minlmstate &state, const double teststep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Results of OptGuard integrity check, should be called after optimization
session is over.
OptGuard checks analytic Jacobian against reference value obtained by
numerical differentiation with user-specified step.
NOTE: other optimizers perform additional OptGuard checks for things like
C0/C1-continuity violations. However, LM optimizer can check only
for incorrect Jacobian.
The reason is that unlike line search methods LM optimizer does not
perform extensive evaluations along the line. Thus, we simply do not
have enough data to catch C0/C1-violations.
This check is activated with minlmoptguardgradient() function.
Following flags are set when these errors are suspected:
* rep.badgradsuspected, and additionally:
* rep.badgradfidx for specific function (Jacobian row) suspected
* rep.badgradvidx for specific variable (Jacobian column) suspected
* rep.badgradxbase, a point where gradient/Jacobian is tested
* rep.badgraduser, user-provided gradient/Jacobian
* rep.badgradnum, reference gradient/Jacobian obtained via numerical
differentiation
INPUT PARAMETERS:
state - algorithm state
OUTPUT PARAMETERS:
rep - OptGuard report
-- ALGLIB --
Copyright 21.11.2018 by Bochkanov Sergey
*************************************************************************/
void minlmoptguardresults(const minlmstate &state, optguardreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Levenberg-Marquardt algorithm results
NOTE: if you activated OptGuard integrity checking functionality and want
to get OptGuard report, it can be retrieved with the help of
minlmoptguardresults() function.
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report; includes termination codes and
additional information. Termination codes are listed below,
see comments for this structure for more info.
Termination code is stored in rep.terminationtype field:
* -8 optimizer detected NAN/INF values either in the
function itself, or in its Jacobian
* -3 constraints are inconsistent
* 2 relative step is no more than EpsX.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 8 terminated by user who called minlmrequesttermination().
X contains point which was "current accepted" when
termination request was submitted.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmresults(const minlmstate &state, real_1d_array &x, minlmreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Levenberg-Marquardt algorithm results
Buffered implementation of MinLMResults(), which uses pre-allocated buffer
to store X[]. If buffer size is too small, it resizes buffer. It is
intended to be used in the inner cycles of performance critical algorithms
where array reallocation penalty is too large to be ignored.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmresultsbuf(const minlmstate &state, real_1d_array &x, minlmreport &rep, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine restarts LM algorithm from new point. All optimization
parameters are left unchanged.
This function allows to solve multiple optimization problems (which
must have same number of dimensions) without object reallocation penalty.
INPUT PARAMETERS:
State - structure used for reverse communication previously
allocated with MinLMCreateXXX call.
X - new starting point.
-- ALGLIB --
Copyright 30.07.2010 by Bochkanov Sergey
*************************************************************************/
void minlmrestartfrom(const minlmstate &state, const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This subroutine submits request for termination of running optimizer. It
should be called from user-supplied callback when user decides that it is
time to "smoothly" terminate optimization process. As result, optimizer
stops at point which was "current accepted" when termination request was
submitted and returns error code 8 (successful termination).
INPUT PARAMETERS:
State - optimizer structure
NOTE: after request for termination optimizer may perform several
additional calls to user-supplied callbacks. It does NOT guarantee
to stop immediately - it just guarantees that these additional calls
will be discarded later.
NOTE: calling this function on optimizer which is NOT running will have no
effect.
NOTE: multiple calls to this function are possible. First call is counted,
subsequent calls are silently ignored.
-- ALGLIB --
Copyright 08.10.2014 by Bochkanov Sergey
*************************************************************************/
void minlmrequesttermination(const minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This is obsolete function.
Since ALGLIB 3.3 it is equivalent to MinLMCreateVJ().
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatevgj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatevgj(const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This is obsolete function.
Since ALGLIB 3.3 it is equivalent to MinLMCreateFJ().
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefgj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatefgj(const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function is considered obsolete since ALGLIB 3.1.0 and is present for
backward compatibility only. We recommend to use MinLMCreateVJ, which
provides similar, but more consistent and feature-rich interface.
-- ALGLIB --
Copyright 30.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmcreatefj(const ae_int_t n, const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
void minlmcreatefj(const ae_int_t m, const real_1d_array &x, minlmstate &state, const xparams _xparams = alglib::xdefault);
#endif
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_CQMODELS) || !defined(AE_PARTIAL_BUILD)
void cqminit(ae_int_t n, convexquadraticmodel* s, ae_state *_state);
void cqmseta(convexquadraticmodel* s,
/* Real */ ae_matrix* a,
ae_bool isupper,
double alpha,
ae_state *_state);
void cqmgeta(convexquadraticmodel* s,
/* Real */ ae_matrix* a,
ae_state *_state);
void cqmrewritedensediagonal(convexquadraticmodel* s,
/* Real */ ae_vector* z,
ae_state *_state);
void cqmsetd(convexquadraticmodel* s,
/* Real */ ae_vector* d,
double tau,
ae_state *_state);
void cqmdropa(convexquadraticmodel* s, ae_state *_state);
void cqmsetb(convexquadraticmodel* s,
/* Real */ ae_vector* b,
ae_state *_state);
void cqmsetq(convexquadraticmodel* s,
/* Real */ ae_matrix* q,
/* Real */ ae_vector* r,
ae_int_t k,
double theta,
ae_state *_state);
void cqmsetactiveset(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Boolean */ ae_vector* activeset,
ae_state *_state);
double cqmeval(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmevalx(convexquadraticmodel* s,
/* Real */ ae_vector* x,
double* r,
double* noise,
ae_state *_state);
void cqmgradunconstrained(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* g,
ae_state *_state);
double cqmxtadx2(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* tmp,
ae_state *_state);
void cqmadx(convexquadraticmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state);
ae_bool cqmconstrainedoptimum(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmscalevector(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void cqmgetdiaga(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
double cqmdebugconstrainedevalt(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
double cqmdebugconstrainedevale(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
void _convexquadraticmodel_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _convexquadraticmodel_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _convexquadraticmodel_clear(void* _p);
void _convexquadraticmodel_destroy(void* _p);
#endif
#if defined(AE_COMPILE_OPTGUARDAPI) || !defined(AE_PARTIAL_BUILD)
void optguardinitinternal(optguardreport* rep,
ae_int_t n,
ae_int_t k,
ae_state *_state);
void optguardexportreport(optguardreport* srcrep,
ae_int_t n,
ae_int_t k,
ae_bool badgradhasxj,
optguardreport* dstrep,
ae_state *_state);
void smoothnessmonitorexportc1test0report(optguardnonc1test0report* srcrep,
/* Real */ ae_vector* s,
optguardnonc1test0report* dstrep,
ae_state *_state);
void smoothnessmonitorexportc1test1report(optguardnonc1test1report* srcrep,
/* Real */ ae_vector* s,
optguardnonc1test1report* dstrep,
ae_state *_state);
ae_bool optguardallclear(optguardreport* rep, ae_state *_state);
void _optguardreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _optguardreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _optguardreport_clear(void* _p);
void _optguardreport_destroy(void* _p);
void _optguardnonc0report_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _optguardnonc0report_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _optguardnonc0report_clear(void* _p);
void _optguardnonc0report_destroy(void* _p);
void _optguardnonc1test0report_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _optguardnonc1test0report_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _optguardnonc1test0report_clear(void* _p);
void _optguardnonc1test0report_destroy(void* _p);
void _optguardnonc1test1report_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _optguardnonc1test1report_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _optguardnonc1test1report_clear(void* _p);
void _optguardnonc1test1report_destroy(void* _p);
#endif
#if defined(AE_COMPILE_OPTSERV) || !defined(AE_PARTIAL_BUILD)
void checkbcviolation(/* Boolean */ ae_vector* hasbndl,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* hasbndu,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* s,
ae_bool nonunits,
double* bcerr,
ae_int_t* bcidx,
ae_state *_state);
void checklcviolation(/* Real */ ae_matrix* cleic,
/* Integer */ ae_vector* lcsrcidx,
ae_int_t nec,
ae_int_t nic,
/* Real */ ae_vector* x,
ae_int_t n,
double* lcerr,
ae_int_t* lcidx,
ae_state *_state);
void checknlcviolation(/* Real */ ae_vector* fi,
ae_int_t ng,
ae_int_t nh,
double* nlcerr,
ae_int_t* nlcidx,
ae_state *_state);
void unscaleandchecknlcviolation(/* Real */ ae_vector* fi,
/* Real */ ae_vector* fscales,
ae_int_t ng,
ae_int_t nh,
double* nlcerr,
ae_int_t* nlcidx,
ae_state *_state);
void trimprepare(double f, double* threshold, ae_state *_state);
void trimfunction(double* f,
/* Real */ ae_vector* g,
ae_int_t n,
double threshold,
ae_state *_state);
ae_bool enforceboundaryconstraints(/* Real */ ae_vector* x,
/* Real */ ae_vector* bl,
/* Boolean */ ae_vector* havebl,
/* Real */ ae_vector* bu,
/* Boolean */ ae_vector* havebu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
void projectgradientintobc(/* Real */ ae_vector* x,
/* Real */ ae_vector* g,
/* Real */ ae_vector* bl,
/* Boolean */ ae_vector* havebl,
/* Real */ ae_vector* bu,
/* Boolean */ ae_vector* havebu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
void calculatestepbound(/* Real */ ae_vector* x,
/* Real */ ae_vector* d,
double alpha,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_int_t* variabletofreeze,
double* valuetofreeze,
double* maxsteplen,
ae_state *_state);
ae_int_t postprocessboundedstep(/* Real */ ae_vector* x,
/* Real */ ae_vector* xprev,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_int_t variabletofreeze,
double valuetofreeze,
double steptaken,
double maxsteplen,
ae_state *_state);
void filterdirection(/* Real */ ae_vector* d,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
/* Real */ ae_vector* s,
ae_int_t nmain,
ae_int_t nslack,
double droptol,
ae_state *_state);
ae_int_t numberofchangedconstraints(/* Real */ ae_vector* x,
/* Real */ ae_vector* xprev,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
ae_state *_state);
ae_bool findfeasiblepoint(/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Boolean */ ae_vector* havebndl,
/* Real */ ae_vector* bndu,
/* Boolean */ ae_vector* havebndu,
ae_int_t nmain,
ae_int_t nslack,
/* Real */ ae_matrix* ce,
ae_int_t k,
double epsi,
ae_int_t* qpits,
ae_int_t* gpaits,
ae_state *_state);
ae_bool derivativecheck(double f0,
double df0,
double f1,
double df1,
double f,
double df,
double width,
ae_state *_state);
void estimateparabolicmodel(double absasum,
double absasum2,
double mx,
double mb,
double md,
double d1,
double d2,
ae_int_t* d1est,
ae_int_t* d2est,
ae_state *_state);
void inexactlbfgspreconditioner(/* Real */ ae_vector* s,
ae_int_t n,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t k,
precbuflbfgs* buf,
ae_state *_state);
void preparelowrankpreconditioner(/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t n,
ae_int_t k,
precbuflowrank* buf,
ae_state *_state);
void applylowrankpreconditioner(/* Real */ ae_vector* s,
precbuflowrank* buf,
ae_state *_state);
void smoothnessmonitorinit(smoothnessmonitor* monitor,
ae_int_t n,
ae_int_t k,
ae_bool checksmoothness,
ae_state *_state);
void smoothnessmonitorstartlinesearch(smoothnessmonitor* monitor,
/* Real */ ae_vector* x,
/* Real */ ae_vector* fi,
/* Real */ ae_matrix* jac,
ae_state *_state);
void smoothnessmonitorstartlinesearch1u(smoothnessmonitor* monitor,
/* Real */ ae_vector* s,
/* Real */ ae_vector* invs,
/* Real */ ae_vector* x,
double f0,
/* Real */ ae_vector* j0,
ae_state *_state);
void smoothnessmonitorenqueuepoint(smoothnessmonitor* monitor,
/* Real */ ae_vector* d,
double stp,
/* Real */ ae_vector* x,
/* Real */ ae_vector* fi,
/* Real */ ae_matrix* jac,
ae_state *_state);
void smoothnessmonitorenqueuepoint1u(smoothnessmonitor* monitor,
/* Real */ ae_vector* s,
/* Real */ ae_vector* invs,
/* Real */ ae_vector* d,
double stp,
/* Real */ ae_vector* x,
double f0,
/* Real */ ae_vector* j0,
ae_state *_state);
void smoothnessmonitorfinalizelinesearch(smoothnessmonitor* monitor,
ae_state *_state);
void smoothnessmonitorstartprobing(smoothnessmonitor* monitor,
double stpmax,
ae_int_t nvalues,
double stepscale,
ae_state *_state);
ae_bool smoothnessmonitorprobe(smoothnessmonitor* monitor,
ae_state *_state);
void smoothnessmonitortraceprobingresults(smoothnessmonitor* monitor,
ae_state *_state);
void smoothnessmonitortracestatus(smoothnessmonitor* monitor,
ae_bool callersuggeststrace,
ae_state *_state);
void smoothnessmonitorexportreport(smoothnessmonitor* monitor,
optguardreport* rep,
ae_state *_state);
ae_bool smoothnessmonitorcheckgradientatx0(smoothnessmonitor* monitor,
/* Real */ ae_vector* unscaledx0,
/* Real */ ae_vector* s,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_bool hasboxconstraints,
double teststep,
ae_state *_state);
void _precbuflbfgs_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _precbuflbfgs_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _precbuflbfgs_clear(void* _p);
void _precbuflbfgs_destroy(void* _p);
void _precbuflowrank_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _precbuflowrank_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _precbuflowrank_clear(void* _p);
void _precbuflowrank_destroy(void* _p);
void _smoothnessmonitor_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _smoothnessmonitor_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _smoothnessmonitor_clear(void* _p);
void _smoothnessmonitor_destroy(void* _p);
#endif
#if defined(AE_COMPILE_SNNLS) || !defined(AE_PARTIAL_BUILD)
void snnlsinit(ae_int_t nsmax,
ae_int_t ndmax,
ae_int_t nrmax,
snnlssolver* s,
ae_state *_state);
void snnlssetproblem(snnlssolver* s,
/* Real */ ae_matrix* a,
/* Real */ ae_vector* b,
ae_int_t ns,
ae_int_t nd,
ae_int_t nr,
ae_state *_state);
void snnlsdropnnc(snnlssolver* s, ae_int_t idx, ae_state *_state);
void snnlssolve(snnlssolver* s,
/* Real */ ae_vector* x,
ae_state *_state);
void _snnlssolver_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _snnlssolver_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _snnlssolver_clear(void* _p);
void _snnlssolver_destroy(void* _p);
#endif
#if defined(AE_COMPILE_SACTIVESETS) || !defined(AE_PARTIAL_BUILD)
void sasinit(ae_int_t n, sactiveset* s, ae_state *_state);
void sassetscale(sactiveset* state,
/* Real */ ae_vector* s,
ae_state *_state);
void sassetprecdiag(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sassetbc(sactiveset* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void sassetlc(sactiveset* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void sassetlcx(sactiveset* state,
/* Real */ ae_matrix* cleic,
ae_int_t nec,
ae_int_t nic,
ae_state *_state);
ae_bool sasstartoptimization(sactiveset* state,
/* Real */ ae_vector* x,
ae_state *_state);
void sasexploredirection(sactiveset* state,
/* Real */ ae_vector* d,
double* stpmax,
ae_int_t* cidx,
double* vval,
ae_state *_state);
ae_int_t sasmoveto(sactiveset* state,
/* Real */ ae_vector* xn,
ae_bool needact,
ae_int_t cidx,
double cval,
ae_state *_state);
void sasimmediateactivation(sactiveset* state,
ae_int_t cidx,
double cval,
ae_state *_state);
void sasconstraineddescent(sactiveset* state,
/* Real */ ae_vector* g,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddescentprec(sactiveset* state,
/* Real */ ae_vector* g,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddirection(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sasconstraineddirectionprec(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sascorrection(sactiveset* state,
/* Real */ ae_vector* x,
double* penalty,
ae_state *_state);
double sasactivelcpenalty1(sactiveset* state,
/* Real */ ae_vector* x,
ae_state *_state);
double sasscaledconstrainednorm(sactiveset* state,
/* Real */ ae_vector* d,
ae_state *_state);
void sasstopoptimization(sactiveset* state, ae_state *_state);
void sasreactivateconstraints(sactiveset* state,
/* Real */ ae_vector* gc,
ae_state *_state);
void sasreactivateconstraintsprec(sactiveset* state,
/* Real */ ae_vector* gc,
ae_state *_state);
void sasrebuildbasis(sactiveset* state, ae_state *_state);
void sasappendtobasis(sactiveset* state,
/* Boolean */ ae_vector* newentries,
ae_state *_state);
void _sactiveset_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _sactiveset_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _sactiveset_clear(void* _p);
void _sactiveset_destroy(void* _p);
#endif
#if defined(AE_COMPILE_QQPSOLVER) || !defined(AE_PARTIAL_BUILD)
void qqploaddefaults(ae_int_t n, qqpsettings* s, ae_state *_state);
void qqpcopysettings(qqpsettings* src, qqpsettings* dst, ae_state *_state);
void qqppreallocategrowdense(qqpbuffers* sstate,
ae_int_t nexpected,
ae_int_t ngrowto,
ae_state *_state);
void qqpoptimize(convexquadraticmodel* cqmac,
sparsematrix* sparseac,
/* Real */ ae_matrix* denseac,
ae_int_t akind,
ae_bool isupper,
/* Real */ ae_vector* bc,
/* Real */ ae_vector* bndlc,
/* Real */ ae_vector* bnduc,
/* Real */ ae_vector* sc,
/* Real */ ae_vector* xoriginc,
ae_int_t nc,
qqpsettings* settings,
qqpbuffers* sstate,
/* Real */ ae_vector* xs,
ae_int_t* terminationtype,
ae_state *_state);
void _qqpsettings_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qqpsettings_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qqpsettings_clear(void* _p);
void _qqpsettings_destroy(void* _p);
void _qqpbuffers_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qqpbuffers_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qqpbuffers_clear(void* _p);
void _qqpbuffers_destroy(void* _p);
#endif
#if defined(AE_COMPILE_LPQPSERV) || !defined(AE_PARTIAL_BUILD)
void scaleshiftbcinplace(/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_int_t n,
ae_state *_state);
void scaleshiftdensebrlcinplace(/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
/* Real */ ae_matrix* densea,
/* Real */ ae_vector* ab,
/* Real */ ae_vector* ar,
ae_int_t m,
ae_state *_state);
void scaleshiftmixedbrlcinplace(/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
sparsematrix* sparsea,
ae_int_t msparse,
/* Real */ ae_matrix* densea,
ae_int_t mdense,
/* Real */ ae_vector* ab,
/* Real */ ae_vector* ar,
ae_state *_state);
void scaledenseqpinplace(/* Real */ ae_matrix* densea,
ae_bool isupper,
ae_int_t nmain,
/* Real */ ae_vector* denseb,
ae_int_t ntotal,
/* Real */ ae_vector* s,
ae_state *_state);
void scalesparseqpinplace(/* Real */ ae_vector* s,
ae_int_t n,
sparsematrix* sparsea,
/* Real */ ae_vector* denseb,
ae_state *_state);
void normalizedensebrlcinplace(/* Real */ ae_matrix* densea,
/* Real */ ae_vector* ab,
/* Real */ ae_vector* ar,
ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* rownorms,
ae_bool neednorms,
ae_state *_state);
void normalizemixedbrlcinplace(sparsematrix* sparsea,
ae_int_t msparse,
/* Real */ ae_matrix* densea,
ae_int_t mdense,
/* Real */ ae_vector* ab,
/* Real */ ae_vector* ar,
ae_int_t n,
/* Real */ ae_vector* rownorms,
ae_bool neednorms,
ae_state *_state);
double normalizedenseqpinplace(/* Real */ ae_matrix* densea,
ae_bool isupper,
ae_int_t nmain,
/* Real */ ae_vector* denseb,
ae_int_t ntotal,
ae_state *_state);
double normalizesparseqpinplace(sparsematrix* sparsea,
ae_bool isupper,
/* Real */ ae_vector* denseb,
ae_int_t n,
ae_state *_state);
void unscaleunshiftpointbc(/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
/* Real */ ae_vector* rawbndl,
/* Real */ ae_vector* rawbndu,
/* Real */ ae_vector* sclsftbndl,
/* Real */ ae_vector* sclsftbndu,
/* Boolean */ ae_vector* hasbndl,
/* Boolean */ ae_vector* hasbndu,
/* Real */ ae_vector* x,
ae_int_t n,
ae_state *_state);
#endif
#if defined(AE_COMPILE_VIPMSOLVER) || !defined(AE_PARTIAL_BUILD)
void vipminitdense(vipmstate* state,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
ae_state *_state);
void vipminitdensewithslacks(vipmstate* state,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t nmain,
ae_int_t n,
ae_state *_state);
void vipminitsparse(vipmstate* state,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
ae_state *_state);
void vipmsetquadraticlinear(vipmstate* state,
/* Real */ ae_matrix* denseh,
sparsematrix* sparseh,
ae_int_t hkind,
ae_bool isupper,
/* Real */ ae_vector* c,
ae_state *_state);
void vipmsetconstraints(vipmstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
sparsematrix* sparsea,
ae_int_t msparse,
/* Real */ ae_matrix* densea,
ae_int_t mdense,
/* Real */ ae_vector* cl,
/* Real */ ae_vector* cu,
ae_state *_state);
void vipmsetcond(vipmstate* state,
double epsp,
double epsd,
double epsgap,
ae_state *_state);
void vipmoptimize(vipmstate* state,
/* Real */ ae_vector* xs,
/* Real */ ae_vector* lagbc,
/* Real */ ae_vector* laglc,
ae_int_t* terminationtype,
ae_state *_state);
void _vipmvars_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _vipmvars_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _vipmvars_clear(void* _p);
void _vipmvars_destroy(void* _p);
void _vipmstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _vipmstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _vipmstate_clear(void* _p);
void _vipmstate_destroy(void* _p);
#endif
#if defined(AE_COMPILE_NLCSQP) || !defined(AE_PARTIAL_BUILD)
void minsqpinitbuf(/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* x0,
ae_int_t n,
/* Real */ ae_matrix* cleic,
/* Integer */ ae_vector* lcsrcidx,
ae_int_t nec,
ae_int_t nic,
ae_int_t nlec,
ae_int_t nlic,
double epsx,
ae_int_t maxits,
minsqpstate* state,
ae_state *_state);
ae_bool minsqpiteration(minsqpstate* state,
smoothnessmonitor* smonitor,
ae_bool userterminationneeded,
ae_state *_state);
void _minsqpsubsolver_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minsqpsubsolver_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minsqpsubsolver_clear(void* _p);
void _minsqpsubsolver_destroy(void* _p);
void _minsqptmplagrangian_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minsqptmplagrangian_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minsqptmplagrangian_clear(void* _p);
void _minsqptmplagrangian_destroy(void* _p);
void _minsqptmpmerit_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minsqptmpmerit_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minsqptmpmerit_clear(void* _p);
void _minsqptmpmerit_destroy(void* _p);
void _minsqpmeritphasestate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minsqpmeritphasestate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minsqpmeritphasestate_clear(void* _p);
void _minsqpmeritphasestate_destroy(void* _p);
void _minsqpstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minsqpstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minsqpstate_clear(void* _p);
void _minsqpstate_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINLBFGS) || !defined(AE_PARTIAL_BUILD)
void minlbfgscreate(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlbfgsstate* state,
ae_state *_state);
void minlbfgscreatef(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
double diffstep,
minlbfgsstate* state,
ae_state *_state);
void minlbfgssetcond(minlbfgsstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minlbfgssetxrep(minlbfgsstate* state,
ae_bool needxrep,
ae_state *_state);
void minlbfgssetstpmax(minlbfgsstate* state,
double stpmax,
ae_state *_state);
void minlbfgssetscale(minlbfgsstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minlbfgscreatex(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
ae_int_t flags,
double diffstep,
minlbfgsstate* state,
ae_state *_state);
void minlbfgssetprecdefault(minlbfgsstate* state, ae_state *_state);
void minlbfgssetpreccholesky(minlbfgsstate* state,
/* Real */ ae_matrix* p,
ae_bool isupper,
ae_state *_state);
void minlbfgssetprecdiag(minlbfgsstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void minlbfgssetprecscale(minlbfgsstate* state, ae_state *_state);
void minlbfgssetprecrankklbfgsfast(minlbfgsstate* state,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t cnt,
ae_state *_state);
void minlbfgssetpreclowrankexact(minlbfgsstate* state,
/* Real */ ae_vector* d,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* w,
ae_int_t cnt,
ae_state *_state);
ae_bool minlbfgsiteration(minlbfgsstate* state, ae_state *_state);
void minlbfgsoptguardgradient(minlbfgsstate* state,
double teststep,
ae_state *_state);
void minlbfgsoptguardsmoothness(minlbfgsstate* state,
ae_int_t level,
ae_state *_state);
void minlbfgsoptguardresults(minlbfgsstate* state,
optguardreport* rep,
ae_state *_state);
void minlbfgsoptguardnonc1test0results(minlbfgsstate* state,
optguardnonc1test0report* strrep,
optguardnonc1test0report* lngrep,
ae_state *_state);
void minlbfgsoptguardnonc1test1results(minlbfgsstate* state,
optguardnonc1test1report* strrep,
optguardnonc1test1report* lngrep,
ae_state *_state);
void minlbfgsresults(minlbfgsstate* state,
/* Real */ ae_vector* x,
minlbfgsreport* rep,
ae_state *_state);
void minlbfgsresultsbuf(minlbfgsstate* state,
/* Real */ ae_vector* x,
minlbfgsreport* rep,
ae_state *_state);
void minlbfgsrestartfrom(minlbfgsstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minlbfgsrequesttermination(minlbfgsstate* state, ae_state *_state);
void _minlbfgsstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlbfgsstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlbfgsstate_clear(void* _p);
void _minlbfgsstate_destroy(void* _p);
void _minlbfgsreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlbfgsreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlbfgsreport_clear(void* _p);
void _minlbfgsreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_QPDENSEAULSOLVER) || !defined(AE_PARTIAL_BUILD)
void qpdenseaulloaddefaults(ae_int_t nmain,
qpdenseaulsettings* s,
ae_state *_state);
void qpdenseauloptimize(convexquadraticmodel* a,
sparsematrix* sparsea,
ae_int_t akind,
ae_bool sparseaupper,
/* Real */ ae_vector* b,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t nn,
/* Real */ ae_matrix* cleic,
ae_int_t dnec,
ae_int_t dnic,
sparsematrix* scleic,
ae_int_t snec,
ae_int_t snic,
ae_bool renormlc,
qpdenseaulsettings* settings,
qpdenseaulbuffers* state,
/* Real */ ae_vector* xs,
/* Real */ ae_vector* lagbc,
/* Real */ ae_vector* laglc,
ae_int_t* terminationtype,
ae_state *_state);
void _qpdenseaulsettings_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qpdenseaulsettings_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qpdenseaulsettings_clear(void* _p);
void _qpdenseaulsettings_destroy(void* _p);
void _qpdenseaulbuffers_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qpdenseaulbuffers_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qpdenseaulbuffers_clear(void* _p);
void _qpdenseaulbuffers_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINBLEIC) || !defined(AE_PARTIAL_BUILD)
void minbleiccreate(ae_int_t n,
/* Real */ ae_vector* x,
minbleicstate* state,
ae_state *_state);
void minbleiccreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minbleicstate* state,
ae_state *_state);
void minbleicsetbc(minbleicstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minbleicsetlc(minbleicstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minbleicsetcond(minbleicstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minbleicsetscale(minbleicstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minbleicsetprecdefault(minbleicstate* state, ae_state *_state);
void minbleicsetprecdiag(minbleicstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void minbleicsetprecscale(minbleicstate* state, ae_state *_state);
void minbleicsetxrep(minbleicstate* state,
ae_bool needxrep,
ae_state *_state);
void minbleicsetdrep(minbleicstate* state,
ae_bool needdrep,
ae_state *_state);
void minbleicsetstpmax(minbleicstate* state,
double stpmax,
ae_state *_state);
ae_bool minbleiciteration(minbleicstate* state, ae_state *_state);
void minbleicoptguardgradient(minbleicstate* state,
double teststep,
ae_state *_state);
void minbleicoptguardsmoothness(minbleicstate* state,
ae_int_t level,
ae_state *_state);
void minbleicoptguardresults(minbleicstate* state,
optguardreport* rep,
ae_state *_state);
void minbleicoptguardnonc1test0results(minbleicstate* state,
optguardnonc1test0report* strrep,
optguardnonc1test0report* lngrep,
ae_state *_state);
void minbleicoptguardnonc1test1results(minbleicstate* state,
optguardnonc1test1report* strrep,
optguardnonc1test1report* lngrep,
ae_state *_state);
void minbleicresults(minbleicstate* state,
/* Real */ ae_vector* x,
minbleicreport* rep,
ae_state *_state);
void minbleicresultsbuf(minbleicstate* state,
/* Real */ ae_vector* x,
minbleicreport* rep,
ae_state *_state);
void minbleicrestartfrom(minbleicstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minbleicrequesttermination(minbleicstate* state, ae_state *_state);
void minbleicemergencytermination(minbleicstate* state, ae_state *_state);
void _minbleicstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minbleicstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbleicstate_clear(void* _p);
void _minbleicstate_destroy(void* _p);
void _minbleicreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minbleicreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbleicreport_clear(void* _p);
void _minbleicreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_QPBLEICSOLVER) || !defined(AE_PARTIAL_BUILD)
void qpbleicloaddefaults(ae_int_t nmain,
qpbleicsettings* s,
ae_state *_state);
void qpbleiccopysettings(qpbleicsettings* src,
qpbleicsettings* dst,
ae_state *_state);
void qpbleicoptimize(convexquadraticmodel* a,
sparsematrix* sparsea,
ae_int_t akind,
ae_bool sparseaupper,
double absasum,
double absasum2,
/* Real */ ae_vector* b,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* xorigin,
ae_int_t n,
/* Real */ ae_matrix* cleic,
ae_int_t nec,
ae_int_t nic,
qpbleicsettings* settings,
qpbleicbuffers* sstate,
ae_bool* firstcall,
/* Real */ ae_vector* xs,
ae_int_t* terminationtype,
ae_state *_state);
void _qpbleicsettings_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qpbleicsettings_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qpbleicsettings_clear(void* _p);
void _qpbleicsettings_destroy(void* _p);
void _qpbleicbuffers_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _qpbleicbuffers_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _qpbleicbuffers_clear(void* _p);
void _qpbleicbuffers_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINQP) || !defined(AE_PARTIAL_BUILD)
void minqpcreate(ae_int_t n, minqpstate* state, ae_state *_state);
void minqpsetlinearterm(minqpstate* state,
/* Real */ ae_vector* b,
ae_state *_state);
void minqpsetquadraticterm(minqpstate* state,
/* Real */ ae_matrix* a,
ae_bool isupper,
ae_state *_state);
void minqpsetquadratictermsparse(minqpstate* state,
sparsematrix* a,
ae_bool isupper,
ae_state *_state);
void minqpsetstartingpoint(minqpstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minqpsetorigin(minqpstate* state,
/* Real */ ae_vector* xorigin,
ae_state *_state);
void minqpsetscale(minqpstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minqpsetscaleautodiag(minqpstate* state, ae_state *_state);
void minqpsetalgobleic(minqpstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minqpsetalgodenseaul(minqpstate* state,
double epsx,
double rho,
ae_int_t itscnt,
ae_state *_state);
void minqpsetalgodenseipm(minqpstate* state, double eps, ae_state *_state);
void minqpsetalgosparseipm(minqpstate* state,
double eps,
ae_state *_state);
void minqpsetalgoquickqp(minqpstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxouterits,
ae_bool usenewton,
ae_state *_state);
void minqpsetbc(minqpstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minqpsetbcall(minqpstate* state,
double bndl,
double bndu,
ae_state *_state);
void minqpsetbci(minqpstate* state,
ae_int_t i,
double bndl,
double bndu,
ae_state *_state);
void minqpsetlc(minqpstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minqpsetlcsparse(minqpstate* state,
sparsematrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minqpsetlcmixed(minqpstate* state,
sparsematrix* sparsec,
/* Integer */ ae_vector* sparsect,
ae_int_t sparsek,
/* Real */ ae_matrix* densec,
/* Integer */ ae_vector* densect,
ae_int_t densek,
ae_state *_state);
void minqpsetlcmixedlegacy(minqpstate* state,
/* Real */ ae_matrix* densec,
/* Integer */ ae_vector* densect,
ae_int_t densek,
sparsematrix* sparsec,
/* Integer */ ae_vector* sparsect,
ae_int_t sparsek,
ae_state *_state);
void minqpsetlc2dense(minqpstate* state,
/* Real */ ae_matrix* a,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_int_t k,
ae_state *_state);
void minqpsetlc2(minqpstate* state,
sparsematrix* a,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_int_t k,
ae_state *_state);
void minqpsetlc2mixed(minqpstate* state,
sparsematrix* sparsea,
ae_int_t ksparse,
/* Real */ ae_matrix* densea,
ae_int_t kdense,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_state *_state);
void minqpaddlc2dense(minqpstate* state,
/* Real */ ae_vector* a,
double al,
double au,
ae_state *_state);
void minqpaddlc2(minqpstate* state,
/* Integer */ ae_vector* idxa,
/* Real */ ae_vector* vala,
ae_int_t nnz,
double al,
double au,
ae_state *_state);
void minqpoptimize(minqpstate* state, ae_state *_state);
void minqpresults(minqpstate* state,
/* Real */ ae_vector* x,
minqpreport* rep,
ae_state *_state);
void minqpresultsbuf(minqpstate* state,
/* Real */ ae_vector* x,
minqpreport* rep,
ae_state *_state);
void minqpsetlineartermfast(minqpstate* state,
/* Real */ ae_vector* b,
ae_state *_state);
void minqpsetquadratictermfast(minqpstate* state,
/* Real */ ae_matrix* a,
ae_bool isupper,
double s,
ae_state *_state);
void minqprewritediagonal(minqpstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minqpsetstartingpointfast(minqpstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minqpsetoriginfast(minqpstate* state,
/* Real */ ae_vector* xorigin,
ae_state *_state);
void _minqpstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minqpstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minqpstate_clear(void* _p);
void _minqpstate_destroy(void* _p);
void _minqpreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minqpreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minqpreport_clear(void* _p);
void _minqpreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_REVISEDDUALSIMPLEX) || !defined(AE_PARTIAL_BUILD)
void dsssettingsinit(dualsimplexsettings* settings, ae_state *_state);
void dssinit(ae_int_t n, dualsimplexstate* s, ae_state *_state);
void dsssetproblem(dualsimplexstate* state,
/* Real */ ae_vector* c,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* sv,
/* Real */ ae_matrix* densea,
sparsematrix* sparsea,
ae_int_t akind,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_int_t k,
dualsimplexbasis* proposedbasis,
ae_int_t basisinittype,
dualsimplexsettings* settings,
ae_state *_state);
void dssexportbasis(dualsimplexstate* state,
dualsimplexbasis* basis,
ae_state *_state);
void dssoptimize(dualsimplexstate* state,
dualsimplexsettings* settings,
ae_state *_state);
void _dualsimplexsettings_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _dualsimplexsettings_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _dualsimplexsettings_clear(void* _p);
void _dualsimplexsettings_destroy(void* _p);
void _dualsimplexbasis_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _dualsimplexbasis_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _dualsimplexbasis_clear(void* _p);
void _dualsimplexbasis_destroy(void* _p);
void _dualsimplexsubproblem_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _dualsimplexsubproblem_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _dualsimplexsubproblem_clear(void* _p);
void _dualsimplexsubproblem_destroy(void* _p);
void _dualsimplexstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _dualsimplexstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _dualsimplexstate_clear(void* _p);
void _dualsimplexstate_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINLP) || !defined(AE_PARTIAL_BUILD)
void minlpcreate(ae_int_t n, minlpstate* state, ae_state *_state);
void minlpsetcost(minlpstate* state,
/* Real */ ae_vector* c,
ae_state *_state);
void minlpsetscale(minlpstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minlpsetbc(minlpstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minlpsetbcall(minlpstate* state,
double bndl,
double bndu,
ae_state *_state);
void minlpsetbci(minlpstate* state,
ae_int_t i,
double bndl,
double bndu,
ae_state *_state);
void minlpsetlc(minlpstate* state,
/* Real */ ae_matrix* a,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minlpsetlc2dense(minlpstate* state,
/* Real */ ae_matrix* a,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_int_t k,
ae_state *_state);
void minlpsetlc2(minlpstate* state,
sparsematrix* a,
/* Real */ ae_vector* al,
/* Real */ ae_vector* au,
ae_int_t k,
ae_state *_state);
void minlpaddlc2dense(minlpstate* state,
/* Real */ ae_vector* a,
double al,
double au,
ae_state *_state);
void minlpaddlc2(minlpstate* state,
/* Integer */ ae_vector* idxa,
/* Real */ ae_vector* vala,
ae_int_t nnz,
double al,
double au,
ae_state *_state);
void minlpoptimize(minlpstate* state, ae_state *_state);
void minlpresults(minlpstate* state,
/* Real */ ae_vector* x,
minlpreport* rep,
ae_state *_state);
void minlpresultsbuf(minlpstate* state,
/* Real */ ae_vector* x,
minlpreport* rep,
ae_state *_state);
void _minlpstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlpstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlpstate_clear(void* _p);
void _minlpstate_destroy(void* _p);
void _minlpreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlpreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlpreport_clear(void* _p);
void _minlpreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_NLCSLP) || !defined(AE_PARTIAL_BUILD)
void minslpinitbuf(/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
/* Real */ ae_vector* s,
/* Real */ ae_vector* x0,
ae_int_t n,
/* Real */ ae_matrix* cleic,
/* Integer */ ae_vector* lcsrcidx,
ae_int_t nec,
ae_int_t nic,
ae_int_t nlec,
ae_int_t nlic,
double epsx,
ae_int_t maxits,
minslpstate* state,
ae_state *_state);
ae_bool minslpiteration(minslpstate* state,
smoothnessmonitor* smonitor,
ae_bool userterminationneeded,
ae_state *_state);
void _minslpsubsolver_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslpsubsolver_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslpsubsolver_clear(void* _p);
void _minslpsubsolver_destroy(void* _p);
void _minslptmplagrangian_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslptmplagrangian_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslptmplagrangian_clear(void* _p);
void _minslptmplagrangian_destroy(void* _p);
void _minslptmpmerit_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslptmpmerit_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslptmpmerit_clear(void* _p);
void _minslptmpmerit_destroy(void* _p);
void _minslpphase13state_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslpphase13state_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslpphase13state_clear(void* _p);
void _minslpphase13state_destroy(void* _p);
void _minslpphase2state_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslpphase2state_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslpphase2state_clear(void* _p);
void _minslpphase2state_destroy(void* _p);
void _minslpstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minslpstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minslpstate_clear(void* _p);
void _minslpstate_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINNLC) || !defined(AE_PARTIAL_BUILD)
void minnlccreate(ae_int_t n,
/* Real */ ae_vector* x,
minnlcstate* state,
ae_state *_state);
void minnlccreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minnlcstate* state,
ae_state *_state);
void minnlcsetbc(minnlcstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minnlcsetlc(minnlcstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minnlcsetnlc(minnlcstate* state,
ae_int_t nlec,
ae_int_t nlic,
ae_state *_state);
void minnlcsetcond(minnlcstate* state,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minnlcsetscale(minnlcstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minnlcsetprecinexact(minnlcstate* state, ae_state *_state);
void minnlcsetprecexactlowrank(minnlcstate* state,
ae_int_t updatefreq,
ae_state *_state);
void minnlcsetprecexactrobust(minnlcstate* state,
ae_int_t updatefreq,
ae_state *_state);
void minnlcsetprecnone(minnlcstate* state, ae_state *_state);
void minnlcsetstpmax(minnlcstate* state, double stpmax, ae_state *_state);
void minnlcsetalgoaul(minnlcstate* state,
double rho,
ae_int_t itscnt,
ae_state *_state);
void minnlcsetalgoslp(minnlcstate* state, ae_state *_state);
void minnlcsetalgosqp(minnlcstate* state, ae_state *_state);
void minnlcsetxrep(minnlcstate* state, ae_bool needxrep, ae_state *_state);
ae_bool minnlciteration(minnlcstate* state, ae_state *_state);
void minnlcoptguardgradient(minnlcstate* state,
double teststep,
ae_state *_state);
void minnlcoptguardsmoothness(minnlcstate* state,
ae_int_t level,
ae_state *_state);
void minnlcoptguardresults(minnlcstate* state,
optguardreport* rep,
ae_state *_state);
void minnlcoptguardnonc1test0results(minnlcstate* state,
optguardnonc1test0report* strrep,
optguardnonc1test0report* lngrep,
ae_state *_state);
void minnlcoptguardnonc1test1results(minnlcstate* state,
optguardnonc1test1report* strrep,
optguardnonc1test1report* lngrep,
ae_state *_state);
void minnlcresults(minnlcstate* state,
/* Real */ ae_vector* x,
minnlcreport* rep,
ae_state *_state);
void minnlcresultsbuf(minnlcstate* state,
/* Real */ ae_vector* x,
minnlcreport* rep,
ae_state *_state);
void minnlcrequesttermination(minnlcstate* state, ae_state *_state);
void minnlcrestartfrom(minnlcstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minnlcequalitypenaltyfunction(double alpha,
double* f,
double* df,
double* d2f,
ae_state *_state);
void minnlcinequalitypenaltyfunction(double alpha,
double stabilizingpoint,
double* f,
double* df,
double* d2f,
ae_state *_state);
void minnlcinequalityshiftfunction(double alpha,
double* f,
double* df,
double* d2f,
ae_state *_state);
void _minnlcstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minnlcstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minnlcstate_clear(void* _p);
void _minnlcstate_destroy(void* _p);
void _minnlcreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minnlcreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minnlcreport_clear(void* _p);
void _minnlcreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINBC) || !defined(AE_PARTIAL_BUILD)
void minbccreate(ae_int_t n,
/* Real */ ae_vector* x,
minbcstate* state,
ae_state *_state);
void minbccreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minbcstate* state,
ae_state *_state);
void minbcsetbc(minbcstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minbcsetcond(minbcstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minbcsetscale(minbcstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minbcsetprecdefault(minbcstate* state, ae_state *_state);
void minbcsetprecdiag(minbcstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void minbcsetprecscale(minbcstate* state, ae_state *_state);
void minbcsetxrep(minbcstate* state, ae_bool needxrep, ae_state *_state);
void minbcsetstpmax(minbcstate* state, double stpmax, ae_state *_state);
ae_bool minbciteration(minbcstate* state, ae_state *_state);
void minbcoptguardgradient(minbcstate* state,
double teststep,
ae_state *_state);
void minbcoptguardsmoothness(minbcstate* state,
ae_int_t level,
ae_state *_state);
void minbcoptguardresults(minbcstate* state,
optguardreport* rep,
ae_state *_state);
void minbcoptguardnonc1test0results(minbcstate* state,
optguardnonc1test0report* strrep,
optguardnonc1test0report* lngrep,
ae_state *_state);
void minbcoptguardnonc1test1results(minbcstate* state,
optguardnonc1test1report* strrep,
optguardnonc1test1report* lngrep,
ae_state *_state);
void minbcresults(minbcstate* state,
/* Real */ ae_vector* x,
minbcreport* rep,
ae_state *_state);
void minbcresultsbuf(minbcstate* state,
/* Real */ ae_vector* x,
minbcreport* rep,
ae_state *_state);
void minbcrestartfrom(minbcstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minbcrequesttermination(minbcstate* state, ae_state *_state);
void _minbcstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minbcstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbcstate_clear(void* _p);
void _minbcstate_destroy(void* _p);
void _minbcreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minbcreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbcreport_clear(void* _p);
void _minbcreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINNS) || !defined(AE_PARTIAL_BUILD)
void minnscreate(ae_int_t n,
/* Real */ ae_vector* x,
minnsstate* state,
ae_state *_state);
void minnscreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
minnsstate* state,
ae_state *_state);
void minnssetbc(minnsstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minnssetlc(minnsstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minnssetnlc(minnsstate* state,
ae_int_t nlec,
ae_int_t nlic,
ae_state *_state);
void minnssetcond(minnsstate* state,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minnssetscale(minnsstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minnssetalgoags(minnsstate* state,
double radius,
double penalty,
ae_state *_state);
void minnssetxrep(minnsstate* state, ae_bool needxrep, ae_state *_state);
void minnsrequesttermination(minnsstate* state, ae_state *_state);
ae_bool minnsiteration(minnsstate* state, ae_state *_state);
void minnsresults(minnsstate* state,
/* Real */ ae_vector* x,
minnsreport* rep,
ae_state *_state);
void minnsresultsbuf(minnsstate* state,
/* Real */ ae_vector* x,
minnsreport* rep,
ae_state *_state);
void minnsrestartfrom(minnsstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void _minnsqp_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minnsqp_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minnsqp_clear(void* _p);
void _minnsqp_destroy(void* _p);
void _minnsstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minnsstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minnsstate_clear(void* _p);
void _minnsstate_destroy(void* _p);
void _minnsreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minnsreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minnsreport_clear(void* _p);
void _minnsreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINCOMP) || !defined(AE_PARTIAL_BUILD)
void minlbfgssetdefaultpreconditioner(minlbfgsstate* state,
ae_state *_state);
void minlbfgssetcholeskypreconditioner(minlbfgsstate* state,
/* Real */ ae_matrix* p,
ae_bool isupper,
ae_state *_state);
void minbleicsetbarrierwidth(minbleicstate* state,
double mu,
ae_state *_state);
void minbleicsetbarrierdecay(minbleicstate* state,
double mudecay,
ae_state *_state);
void minasacreate(ae_int_t n,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
minasastate* state,
ae_state *_state);
void minasasetcond(minasastate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minasasetxrep(minasastate* state, ae_bool needxrep, ae_state *_state);
void minasasetalgorithm(minasastate* state,
ae_int_t algotype,
ae_state *_state);
void minasasetstpmax(minasastate* state, double stpmax, ae_state *_state);
ae_bool minasaiteration(minasastate* state, ae_state *_state);
void minasaresults(minasastate* state,
/* Real */ ae_vector* x,
minasareport* rep,
ae_state *_state);
void minasaresultsbuf(minasastate* state,
/* Real */ ae_vector* x,
minasareport* rep,
ae_state *_state);
void minasarestartfrom(minasastate* state,
/* Real */ ae_vector* x,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void _minasastate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minasastate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minasastate_clear(void* _p);
void _minasastate_destroy(void* _p);
void _minasareport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minasareport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minasareport_clear(void* _p);
void _minasareport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINCG) || !defined(AE_PARTIAL_BUILD)
void mincgcreate(ae_int_t n,
/* Real */ ae_vector* x,
mincgstate* state,
ae_state *_state);
void mincgcreatef(ae_int_t n,
/* Real */ ae_vector* x,
double diffstep,
mincgstate* state,
ae_state *_state);
void mincgsetcond(mincgstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void mincgsetscale(mincgstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void mincgsetxrep(mincgstate* state, ae_bool needxrep, ae_state *_state);
void mincgsetdrep(mincgstate* state, ae_bool needdrep, ae_state *_state);
void mincgsetcgtype(mincgstate* state, ae_int_t cgtype, ae_state *_state);
void mincgsetstpmax(mincgstate* state, double stpmax, ae_state *_state);
void mincgsuggeststep(mincgstate* state, double stp, ae_state *_state);
double mincglastgoodstep(mincgstate* state, ae_state *_state);
void mincgsetprecdefault(mincgstate* state, ae_state *_state);
void mincgsetprecdiag(mincgstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void mincgsetprecscale(mincgstate* state, ae_state *_state);
ae_bool mincgiteration(mincgstate* state, ae_state *_state);
void mincgoptguardgradient(mincgstate* state,
double teststep,
ae_state *_state);
void mincgoptguardsmoothness(mincgstate* state,
ae_int_t level,
ae_state *_state);
void mincgoptguardresults(mincgstate* state,
optguardreport* rep,
ae_state *_state);
void mincgoptguardnonc1test0results(mincgstate* state,
optguardnonc1test0report* strrep,
optguardnonc1test0report* lngrep,
ae_state *_state);
void mincgoptguardnonc1test1results(mincgstate* state,
optguardnonc1test1report* strrep,
optguardnonc1test1report* lngrep,
ae_state *_state);
void mincgresults(mincgstate* state,
/* Real */ ae_vector* x,
mincgreport* rep,
ae_state *_state);
void mincgresultsbuf(mincgstate* state,
/* Real */ ae_vector* x,
mincgreport* rep,
ae_state *_state);
void mincgrestartfrom(mincgstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void mincgrequesttermination(mincgstate* state, ae_state *_state);
void mincgsetprecdiagfast(mincgstate* state,
/* Real */ ae_vector* d,
ae_state *_state);
void mincgsetpreclowrankfast(mincgstate* state,
/* Real */ ae_vector* d1,
/* Real */ ae_vector* c,
/* Real */ ae_matrix* v,
ae_int_t vcnt,
ae_state *_state);
void mincgsetprecvarpart(mincgstate* state,
/* Real */ ae_vector* d2,
ae_state *_state);
void _mincgstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _mincgstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _mincgstate_clear(void* _p);
void _mincgstate_destroy(void* _p);
void _mincgreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _mincgreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _mincgreport_clear(void* _p);
void _mincgreport_destroy(void* _p);
#endif
#if defined(AE_COMPILE_MINLM) || !defined(AE_PARTIAL_BUILD)
void minlmcreatevj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatev(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
double diffstep,
minlmstate* state,
ae_state *_state);
void minlmcreatefgh(ae_int_t n,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmsetcond(minlmstate* state,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minlmsetxrep(minlmstate* state, ae_bool needxrep, ae_state *_state);
void minlmsetstpmax(minlmstate* state, double stpmax, ae_state *_state);
void minlmsetscale(minlmstate* state,
/* Real */ ae_vector* s,
ae_state *_state);
void minlmsetbc(minlmstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minlmsetlc(minlmstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state);
void minlmsetacctype(minlmstate* state,
ae_int_t acctype,
ae_state *_state);
ae_bool minlmiteration(minlmstate* state, ae_state *_state);
void minlmoptguardgradient(minlmstate* state,
double teststep,
ae_state *_state);
void minlmoptguardresults(minlmstate* state,
optguardreport* rep,
ae_state *_state);
void minlmresults(minlmstate* state,
/* Real */ ae_vector* x,
minlmreport* rep,
ae_state *_state);
void minlmresultsbuf(minlmstate* state,
/* Real */ ae_vector* x,
minlmreport* rep,
ae_state *_state);
void minlmrestartfrom(minlmstate* state,
/* Real */ ae_vector* x,
ae_state *_state);
void minlmrequesttermination(minlmstate* state, ae_state *_state);
void minlmcreatevgj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatefgj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void minlmcreatefj(ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x,
minlmstate* state,
ae_state *_state);
void _minlmstepfinder_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlmstepfinder_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlmstepfinder_clear(void* _p);
void _minlmstepfinder_destroy(void* _p);
void _minlmstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlmstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlmstate_clear(void* _p);
void _minlmstate_destroy(void* _p);
void _minlmreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
void _minlmreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlmreport_clear(void* _p);
void _minlmreport_destroy(void* _p);
#endif
}
#endif
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