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psdlag-agn/psdlag/src/optimization.h
caes 49622ad300 added psdlag source code
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/*************************************************************************
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
{
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;
typedef struct
{
ae_int_t ns;
ae_int_t nd;
ae_int_t nr;
ae_matrix densea;
ae_vector b;
ae_vector nnc;
ae_int_t refinementits;
double debugflops;
ae_int_t debugmaxnewton;
ae_vector xn;
ae_matrix tmpz;
ae_matrix tmpca;
ae_vector g;
ae_vector d;
ae_vector dx;
ae_vector diagaa;
ae_vector cb;
ae_vector cx;
ae_vector cborg;
ae_vector columnmap;
ae_vector rowmap;
ae_vector tmpcholesky;
ae_vector r;
} snnlssolver;
typedef struct
{
ae_int_t n;
ae_int_t algostate;
ae_vector xc;
ae_bool hasxc;
ae_vector s;
ae_vector h;
ae_vector activeset;
ae_bool basisisready;
ae_matrix sbasis;
ae_matrix pbasis;
ae_matrix ibasis;
ae_int_t basissize;
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 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;
} sactiveset;
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_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;
double teststep;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
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;
} mincgstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
} mincgreport;
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 lbfgssearch;
ae_bool boundedstep;
double teststep;
rcommstate rstate;
ae_vector gc;
ae_vector xn;
ae_vector gn;
ae_vector xp;
ae_vector gp;
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_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_int_t k;
ae_int_t q;
ae_int_t p;
ae_vector rho;
ae_matrix yk;
ae_matrix sk;
ae_vector theta;
} 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;
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 theta;
ae_vector d;
double stp;
ae_vector work;
double fold;
double trimthreshold;
ae_int_t prectype;
double gammak;
ae_matrix denseh;
ae_vector diagh;
double fbase;
double fm2;
double fm1;
double fp1;
double fp2;
ae_vector autobuf;
ae_vector x;
double f;
ae_vector g;
ae_bool needf;
ae_bool needfg;
ae_bool xupdated;
double teststep;
rcommstate rstate;
ae_int_t repiterationscount;
ae_int_t repnfev;
ae_int_t repvaridx;
ae_int_t repterminationtype;
linminstate lstate;
} minlbfgsstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nfev;
ae_int_t varidx;
ae_int_t terminationtype;
} minlbfgsreport;
typedef struct
{
ae_int_t n;
ae_int_t algokind;
ae_int_t akind;
convexquadraticmodel a;
sparsematrix sparsea;
ae_bool sparseaupper;
double anorm;
ae_vector b;
ae_vector bndl;
ae_vector bndu;
ae_vector s;
ae_vector havebndl;
ae_vector havebndu;
ae_vector xorigin;
ae_vector startx;
ae_bool havex;
ae_matrix cleic;
ae_int_t nec;
ae_int_t nic;
double bleicepsg;
double bleicepsf;
double bleicepsx;
ae_int_t bleicmaxits;
sactiveset sas;
ae_vector gc;
ae_vector xn;
ae_vector pg;
ae_vector workbndl;
ae_vector workbndu;
ae_matrix workcleic;
ae_vector xs;
ae_int_t repinneriterationscount;
ae_int_t repouteriterationscount;
ae_int_t repncholesky;
ae_int_t repnmv;
ae_int_t repterminationtype;
double debugphase1flops;
double debugphase2flops;
double debugphase3flops;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmpb;
ae_vector rctmpg;
ae_vector tmpi;
normestimatorstate estimator;
minbleicstate solver;
minbleicreport solverrep;
} minqpstate;
typedef struct
{
ae_int_t inneriterationscount;
ae_int_t outeriterationscount;
ae_int_t nmv;
ae_int_t ncholesky;
ae_int_t terminationtype;
} minqpreport;
typedef struct
{
ae_int_t n;
ae_int_t m;
double diffstep;
double epsg;
double epsf;
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_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;
double lambdav;
double nu;
ae_int_t modelage;
ae_vector xdir;
ae_vector deltax;
ae_vector deltaf;
ae_bool deltaxready;
ae_bool deltafready;
double teststep;
ae_int_t repiterationscount;
ae_int_t repterminationtype;
ae_int_t repfuncidx;
ae_int_t repvaridx;
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;
} minlmstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t terminationtype;
ae_int_t funcidx;
ae_int_t varidx;
ae_int_t nfunc;
ae_int_t njac;
ae_int_t ngrad;
ae_int_t nhess;
ae_int_t ncholesky;
} minlmreport;
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;
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{
/*************************************************************************
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;
};
/*************************************************************************
*************************************************************************/
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 &varidx;
ae_int_t &terminationtype;
};
/*************************************************************************
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:
-7 gradient verification failed.
See MinBLEICSetGradientCheck() for more information.
-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.
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;
};
/*************************************************************************
*************************************************************************/
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;
};
/*************************************************************************
*************************************************************************/
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 &varidx;
ae_int_t &terminationtype;
};
/*************************************************************************
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)
Completion codes:
* -5 inappropriate solver was used:
* Cholesky solver for semidefinite or indefinite problems
* Cholesky solver for problems with non-boundary constraints
* -4 BLEIC-QP algorithm 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
* 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 _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;
};
/*************************************************************************
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:
* -7 derivative correctness check failed;
see Rep.WrongNum, Rep.WrongI, Rep.WrongJ for
more information.
* 1 relative function improvement is no more than
EpsF.
* 2 relative step is no more than EpsX.
* 4 gradient is no more than EpsG.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
* 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 &funcidx;
ae_int_t &varidx;
ae_int_t &nfunc;
ae_int_t &njac;
ae_int_t &ngrad;
ae_int_t &nhess;
ae_int_t &ncholesky;
};
/*************************************************************************
*************************************************************************/
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;
};
/*************************************************************************
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);
void mincgcreate(const real_1d_array &x, mincgstate &state);
/*************************************************************************
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);
void mincgcreatef(const real_1d_array &x, const double diffstep, mincgstate &state);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
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);
/*************************************************************************
Conjugate gradient results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinCGOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] 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
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinCGSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 31.05.2012 by Bochkanov Sergey
*************************************************************************/
void mincgsetgradientcheck(const mincgstate &state, const double teststep);
/*************************************************************************
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.
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);
void minbleiccreate(const real_1d_array &x, minbleicstate &state);
/*************************************************************************
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);
void minbleiccreatef(const real_1d_array &x, const double diffstep, minbleicstate &state);
/*************************************************************************
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().
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);
/*************************************************************************
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+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 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);
void minbleicsetlc(const minbleicstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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 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 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);
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);
/*************************************************************************
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:
* -7 gradient verification failed.
See MinBLEICSetGradientCheck() for more information.
* -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
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinBLEICOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] 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
* if needed, steps are bounded with respect to constraints on X[]
* 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
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinBLEICSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void minbleicsetgradientcheck(const minbleicstate &state, const double teststep);
/*************************************************************************
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);
void minlbfgscreate(const ae_int_t m, const real_1d_array &x, minlbfgsstate &state);
/*************************************************************************
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);
void minlbfgscreatef(const ae_int_t m, const real_1d_array &x, const double diffstep, minlbfgsstate &state);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
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);
/*************************************************************************
L-BFGS algorithm results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -7 gradient verification failed.
See MinLBFGSSetGradientCheck() for more information.
* -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
* 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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinLBFGSOptimize() is called
* prior to actual optimization, for each component of parameters being
optimized X[i] 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
* if needed, steps are bounded with respect to constraints on X[]
* 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
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) gradient evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided by
some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinLBFGSSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 24.05.2012 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetgradientcheck(const minlbfgsstate &state, const double teststep);
/*************************************************************************
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. You should set quadratic/linear terms with calls to functions
provided by MinQP subpackage.
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);
/*************************************************************************
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);
/*************************************************************************
This function sets dense quadratic term for QP solver. By default,
quadratic term is zero.
SUPPORT BY ALGLIB QP ALGORITHMS:
Dense quadratic term can be handled by any of the QP algorithms supported
by ALGLIB QP Solver.
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<73>t used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn<73>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);
void minqpsetquadraticterm(const minqpstate &state, const real_2d_array &a);
/*************************************************************************
This function sets sparse quadratic term for QP solver. By default,
quadratic term is zero.
SUPPORT BY ALGLIB QP ALGORITHMS:
Sparse quadratic term is supported only by BLEIC-based QP algorithm (one
which is activated by MinQPSetAlgoBLEIC function). Cholesky-based QP algo
won't be able to deal with sparse quadratic term and will terminate
abnormally.
IF YOU CALLED THIS FUNCTION, YOU MUST SWITCH TO BLEIC-BASED QP ALGORITHM
BEFORE CALLING MINQPOPTIMIZE() FUNCTION.
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<73>t used
* if False, symmetric matrix A is given by its lower
triangle, and the upper triangle isn<73>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);
/*************************************************************************
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.
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);
/*************************************************************************
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))
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);
/*************************************************************************
This function sets scaling coefficients.
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
BLEIC-based QP solver uses scale for two purposes:
* to evaluate stopping conditions
* for preconditioning of the underlying BLEIC 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 minqpsetscale(const minqpstate &state, const real_1d_array &s);
/*************************************************************************
This function tells solver to use Cholesky-based algorithm. This algorithm
is active by default.
DESCRIPTION:
Cholesky-based algorithm can be used only for problems which:
* have dense quadratic term, set by MinQPSetQuadraticTerm(), sparse or
structured problems are not supported.
* are strictly convex, i.e. quadratic term is symmetric positive definite,
indefinite or semidefinite problems are not supported by this algorithm.
If anything of what listed above is violated, you may use BLEIC-based QP
algorithm which can be activated by MinQPSetAlgoBLEIC().
BENEFITS AND DRAWBACKS:
This algorithm gives best precision amongst all QP solvers provided by
ALGLIB (Newton iterations have much higher precision than any other
optimization algorithm). This solver also gracefully handles problems with
very large amount of constraints.
Performance of the algorithm is good because internally it uses Level 3
Dense BLAS for its performance-critical parts.
From the other side, algorithm has O(N^3) complexity for unconstrained
problems and up to orders of magnitude slower on constrained problems
(these additional iterations are needed to identify active constraints).
So, its running time depends on number of constraints active at solution.
Furthermore, this algorithm can not solve problems with sparse matrices or
problems with semidefinite/indefinite matrices of any kind (dense/sparse).
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetalgocholesky(const minqpstate &state);
/*************************************************************************
This function tells solver to use BLEIC-based algorithm and sets stopping
criteria for the algorithm.
DESCRIPTION:
BLEIC-based QP algorithm can be used for any kind of QP problems:
* problems with both dense and sparse quadratic terms
* problems with positive definite, semidefinite, indefinite terms
BLEIC-based algorithm can solve even indefinite problems - as long as they
are bounded from below on the feasible set. Of course, global minimum is
found only for positive definite and semidefinite problems. As for
indefinite ones - only local minimum is found.
BENEFITS AND DRAWBACKS:
This algorithm can be used to solve both convex and indefinite QP problems
and it can utilize sparsity of the quadratic term (algorithm calculates
matrix-vector products, which can be performed efficiently in case of
sparse matrix).
Algorithm has iteration cost, which (assuming fixed amount of non-boundary
linear constraints) linearly depends on problem size. Boundary constraints
does not significantly change iteration cost.
Thus, it outperforms Cholesky-based QP algorithm (CQP) on high-dimensional
sparse problems with moderate amount of constraints.
From the other side, unlike CQP solver, this algorithm does NOT make use
of Level 3 Dense BLAS. Thus, its performance on dense problems is inferior
to that of CQP solver.
Its precision is also inferior to that of CQP. CQP performs Newton steps
which are know to achieve very good precision. In many cases Newton step
leads us exactly to the solution. BLEIC-QP performs LBFGS steps, which are
good at detecting neighborhood of the solution, buy need many iterations
to find solution with 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.
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).
IT IS VERY IMPORTANT THAT YOU CALL MinQPSetScale() WHEN YOU USE THIS ALGO!
-- 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);
/*************************************************************************
This function sets boundary constraints for QP solver
Boundary constraints are inactive by default (after initial creation).
After being set, 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: 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].
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpsetbc(const minqpstate &state, const real_1d_array &bndl, const real_1d_array &bndu);
/*************************************************************************
This function sets linear constraints for QP optimizer.
Linear constraints are inactive by default (after initial creation).
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 minor violation (about 10^-10...10^-13)
due to numerical errors.
-- 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);
void minqpsetlc(const minqpstate &state, const real_2d_array &c, const integer_1d_array &ct);
/*************************************************************************
This function solves quadratic programming problem.
You should call it after setting solver options with MinQPSet...() calls.
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);
/*************************************************************************
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. 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:
* -5 inappropriate solver was used:
* Cholesky solver for (semi)indefinite problems
* Cholesky solver for problems with sparse matrix
* -4 BLEIC-QP algorithm 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.
Completion codes specific for Cholesky algorithm:
* 4 successful completion
Completion codes specific for BLEIC-based algorithm:
* 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
-- ALGLIB --
Copyright 11.01.2011 by Bochkanov Sergey
*************************************************************************/
void minqpresults(const minqpstate &state, real_1d_array &x, minqpreport &rep);
/*************************************************************************
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);
/*************************************************************************
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);
void minlmcreatevj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
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);
void minlmcreatev(const ae_int_t m, const real_1d_array &x, const double diffstep, minlmstate &state);
/*************************************************************************
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);
void minlmcreatefgh(const real_1d_array &x, minlmstate &state);
/*************************************************************************
This function sets stopping conditions for Levenberg-Marquardt 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 MinLMSetScale()
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 MinLMSetScale()
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 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 minlmsetcond(const minlmstate &state, const double epsg, const double epsf, const double epsx, const ae_int_t maxits);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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 prohibitive
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 +
DAFAULT 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);
/*************************************************************************
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);
/*************************************************************************
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);
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);
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);
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);
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);
/*************************************************************************
Levenberg-Marquardt algorithm results
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[0..N-1], solution
Rep - optimization report;
see comments for this structure for more info.
-- ALGLIB --
Copyright 10.03.2009 by Bochkanov Sergey
*************************************************************************/
void minlmresults(const minlmstate &state, real_1d_array &x, minlmreport &rep);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
void minlmcreatevgj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
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);
void minlmcreatefgj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
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);
void minlmcreatefj(const ae_int_t m, const real_1d_array &x, minlmstate &state);
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before optimization begins
* MinLMOptimize() is called
* prior to actual optimization, for each function Fi and each component
of parameters being optimized X[j] algorithm performs following steps:
* two trial steps are made to X[j]-TestStep*S[j] and X[j]+TestStep*S[j],
where X[j] is j-th parameter and S[j] is a scale of j-th parameter
* if needed, steps are bounded with respect to constraints on X[]
* Fi(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
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative,
Rep.FuncIdx is set to index of the function.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N (parameters count) Jacobian evaluations. It
is very costly and you should use it only for low dimensional
problems, when you want to be sure that you've correctly
calculated analytic derivatives. You should not use it in the
production code (unless you want to check derivatives provided
by some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with MinLMSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void minlmsetgradientcheck(const minlmstate &state, const double teststep);
/*************************************************************************
Obsolete function, use MinLBFGSSetPrecDefault() instead.
-- ALGLIB --
Copyright 13.10.2010 by Bochkanov Sergey
*************************************************************************/
void minlbfgssetdefaultpreconditioner(const minlbfgsstate &state);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
void minasacreate(const real_1d_array &x, const real_1d_array &bndl, const real_1d_array &bndu, minasastate &state);
/*************************************************************************
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);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetxrep(const minasastate &state, const bool needxrep);
/*************************************************************************
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);
/*************************************************************************
Obsolete optimization algorithm.
Was replaced by MinBLEIC subpackage.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void minasasetstpmax(const minasastate &state, const double stpmax);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
/*************************************************************************
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);
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
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 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 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,
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);
double cqmdebugconstrainedevalt(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
double cqmdebugconstrainedevale(convexquadraticmodel* s,
/* Real */ ae_vector* x,
ae_state *_state);
ae_bool _convexquadraticmodel_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _convexquadraticmodel_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _convexquadraticmodel_clear(void* _p);
void _convexquadraticmodel_destroy(void* _p);
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);
ae_bool _snnlssolver_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _snnlssolver_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _snnlssolver_clear(void* _p);
void _snnlssolver_destroy(void* _p);
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);
ae_bool _sactiveset_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _sactiveset_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _sactiveset_clear(void* _p);
void _sactiveset_destroy(void* _p);
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);
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 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 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 mincgsetgradientcheck(mincgstate* state,
double teststep,
ae_state *_state);
ae_bool _mincgstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _mincgstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _mincgstate_clear(void* _p);
void _mincgstate_destroy(void* _p);
ae_bool _mincgreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _mincgreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _mincgreport_clear(void* _p);
void _mincgreport_destroy(void* _p);
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 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 minbleicemergencytermination(minbleicstate* state, ae_state *_state);
void minbleicsetgradientcheck(minbleicstate* state,
double teststep,
ae_state *_state);
ae_bool _minbleicstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minbleicstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbleicstate_clear(void* _p);
void _minbleicstate_destroy(void* _p);
ae_bool _minbleicreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minbleicreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minbleicreport_clear(void* _p);
void _minbleicreport_destroy(void* _p);
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);
ae_bool minlbfgsiteration(minlbfgsstate* state, 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 minlbfgssetgradientcheck(minlbfgsstate* state,
double teststep,
ae_state *_state);
ae_bool _minlbfgsstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minlbfgsstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlbfgsstate_clear(void* _p);
void _minlbfgsstate_destroy(void* _p);
ae_bool _minlbfgsreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minlbfgsreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlbfgsreport_clear(void* _p);
void _minlbfgsreport_destroy(void* _p);
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 minqpsetalgocholesky(minqpstate* state, ae_state *_state);
void minqpsetalgobleic(minqpstate* state,
double epsg,
double epsf,
double epsx,
ae_int_t maxits,
ae_state *_state);
void minqpsetbc(minqpstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state);
void minqpsetlc(minqpstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
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);
ae_bool _minqpstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minqpstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minqpstate_clear(void* _p);
void _minqpstate_destroy(void* _p);
ae_bool _minqpreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minqpreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minqpreport_clear(void* _p);
void _minqpreport_destroy(void* _p);
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 epsg,
double epsf,
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 minlmsetacctype(minlmstate* state,
ae_int_t acctype,
ae_state *_state);
ae_bool minlmiteration(minlmstate* state, 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 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 minlmsetgradientcheck(minlmstate* state,
double teststep,
ae_state *_state);
ae_bool _minlmstate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minlmstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlmstate_clear(void* _p);
void _minlmstate_destroy(void* _p);
ae_bool _minlmreport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minlmreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minlmreport_clear(void* _p);
void _minlmreport_destroy(void* _p);
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);
ae_bool _minasastate_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _minasastate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic);
void _minasastate_clear(void* _p);
void _minasastate_destroy(void* _p);
ae_bool _minasareport_init(void* _p, ae_state *_state, ae_bool make_automatic);
ae_bool _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
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