implements a direct KKT Solver variant of QPKKTSolverObject More...

#include <QPDirectKKTSolver.hxx>

Inheritance diagram for ConicBundle::QPDirectKKTSolver:

Public Member Functions
virtual void	clear ()
	reset data to empty

	QPDirectKKTSolver (bool in_factorize_ABC=false, CBout *cb=0, int cbinc=-1)
	default constructor

virtual	~QPDirectKKTSolver ()
	virtual destructor

virtual int	QPinit_KKTdata (QPSolverProxObject Hp, QPModelBlockObject model, const CH_Matrix_Classes::Sparsemat A, const CH_Matrix_Classes::Indexmatrix eq_indices)
	returns 1 if this class is not applicable in the current data situation, otherwise it stores the data pointers and these need to stay valid throught the use of the other routines but are not deleted here More...

virtual int	QPinit_KKTsystem (const CH_Matrix_Classes::Matrix &KKTdiagx, const CH_Matrix_Classes::Matrix &KKTdiagy, CH_Matrix_Classes::Real Hfactor, CH_Matrix_Classes::Real prec, QPSolverParameters *params)
	set up the primal dual KKT system for being solved for predictor and corrector rhs in QPsolve_KKTsystem

virtual int	QPsolve_KKTsystem (CH_Matrix_Classes::Matrix &solx, CH_Matrix_Classes::Matrix &soly, const CH_Matrix_Classes::Matrix &primalrhs, const CH_Matrix_Classes::Matrix &dualrhs, CH_Matrix_Classes::Real rhsmu, CH_Matrix_Classes::Real rhscorr, CH_Matrix_Classes::Real prec, QPSolverParameters *params)
	solve the KKTsystem to precision prec for the given right hand sides that have been computed for the value rhsmu of the barrier parameter and in which a rhscorr fraction (out of [0,1] of the corrector term have been included; in iterative solvers solx and soly may be used as starting points

Public Member Functions inherited from ConicBundle::QPKKTSolverObject
	QPKKTSolverObject (CBout *cb=0, int cbinc=-1)
	default constructor

virtual	~QPKKTSolverObject ()
	virtual destructor

virtual CH_Matrix_Classes::Real	QPget_blockH_norm ()
	for judging violation this returns (an estimate of) the norm of the H-row in the latest system

virtual CH_Matrix_Classes::Real	QPget_blockA_norm ()
	for judging violation this returns (an estimate of) the norm of the A-row in the latest system

virtual CH_Matrix_Classes::Integer	QPget_nmult () const
	for evaluation purposes with iterative solvers, return the number of matrix vector multiplications since the latest call to QPinit_KKTsystem (returns 0 for direct solvers)

virtual CH_Matrix_Classes::Real	QPget_condition_number ()
	for evaluation purposes with iterative solvers, return an estimate of the condition number (returns -1. for direct solvers or if not supplied)

virtual CH_Matrix_Classes::Integer	QPget_precond_rank ()
	for evaluation purposes with iterative solvers, return the rank of the precondiontioner used (or the number of n-vector multiplications per call)

virtual CH_Matrix_Classes::Integer	QPget_system_size ()
	for evaluation purposes with iterative solvers, return the size of the system matrix

Public Member Functions inherited from ConicBundle::CBout
virtual void	set_out (std::ostream *out=0, int print_level=1)
	Specifies the output level (out==NULL: no output at all, out!=NULL and level=0: errors and warnings, level>0 increasingly detailed information) More...

virtual void	set_cbout (const CBout *cb, int incr=-1)
	Specifies the output level relative to the given CBout class. More...

void	clear_cbout ()
	reset to default settings (out=0,print_level=1)

	CBout (const CBout *cb=0, int incr=-1)
	calls set_cbout

	CBout (std::ostream *outp, int pl=1)
	initialize correspondingly

	CBout (const CBout &cb, int incr=0)
	copy constructor

virtual bool	cb_out (int pl=-1) const
	Returns true if out!=0 and (pl<print_level), pl<0 should be used for WARNINGS and ERRORS only, pl==0 for usual output.

std::ostream &	get_out () const
	If cb_out() returned true, this returns the output stream, but it will abort if called with out==0.

std::ostream *	get_out_ptr () const
	returns the pointer to the output stream

int	get_print_level () const
	returns the print_level

virtual int	mfile_data (std::ostream &out) const
	writes problem data to the given outstream

Private Member Functions
int	compute_DLR_Schur_complement (CH_Matrix_Classes::Symmatrix &sc)
	computes the Schur complement if Hp->is_DLR()==TRUE, i.e., the quadratic term is representable as diagonal plus low rank

int	compute_dense_Schur_complement (CH_Matrix_Classes::Symmatrix &sc)
	computes the Schur compelement if the quadratic term is only retrievable in dense form

Private Attributes
CH_Matrix_Classes::Integer	dim
	dimension of the quadratic term

CH_Matrix_Classes::Integer	Anr
	number of rows in the constrain matrix =(A==0)?0:A->rowdim();

CH_Matrix_Classes::Integer	bsz
	size of the bundle information in the cutting model

CH_Matrix_Classes::Integer	csz
	number of constraints within the cutting model

const CH_Matrix_Classes::Matrix *	Vp
	used for low rank precondititioning

CH_Matrix_Classes::Real	Hfactor
	scalar factor for H term

CH_Matrix_Classes::Matrix	Diag_inv
	inverse of the KKT diagonal in low rank versions

CH_Matrix_Classes::Symmatrix	Qchol
	Cholesky facotr of KKT Q or of its low rank part.

CH_Matrix_Classes::Symmatrix	Schur_complement
	Schur complement of ABC with Q if no bounds.

CH_Matrix_Classes::Symmatrix	AQiAt_inv
	Cholesky or Aasen factor of ABC with Schur complement.

CH_Matrix_Classes::Symmatrix	CABinvCt_inv
	for forming partial Schur complements

CH_Matrix_Classes::Matrix	LinvC
	for partial Schur complement w.r.t. C block

CH_Matrix_Classes::Indexmatrix	piv
	pivot sequence for Aasen

bool	factorize_ABC
	if true, use Aasen to factor the ABC block

Additional Inherited Members
Protected Attributes inherited from ConicBundle::QPKKTSolverObject
QPSolverProxObject *	Hp
	points to the quadratic cost representation, may NOT be NULL afer init

QPModelBlockObject *	model
	points to the cutting model information, may be NULL

const CH_Matrix_Classes::Sparsemat *	A
	points to a possibly present constraint matrix, may be NULL

const CH_Matrix_Classes::Indexmatrix *	eq_indices
	if not NULL, these rows of A correspond to equations; needed for checking applicability of this Object

CH_Matrix_Classes::Real	blockH_norm
	for judging violation: (an estimate of) the norm of the H-row in the system

CH_Matrix_Classes::Real	blockA_norm
	for judging violation: (an estimate of) the norm of the A-row in the system

Detailed Description

implements a direct KKT Solver variant of QPKKTSolverObject

See the text to QPKKTSolverObject for the terminology of the primal dual KKT System and the general outline.

For solving the system the current class first forms the Schur complement with respect to $H+D_x$ ; this is done in dependence of whether the prox term pointed to by Hp is of the form of Diagonal plus low rank (-> low rank inversion) or dense or other (dense Cholesky). The computed Schur complement matrix [A; B; 0]H^{-1}[A^T,B^T,0] is stored in Schur_complement before it is added to ABC. The code then continues in dependence of the value of factorize_ABC

if factorize_ABC==false, it next factorizes the AB blocks by Cholesky, then the final C block by Cholesky and proceeds in the other direction for solving the system. If in this process a Cholesky factorization fails, the code sets factorize_ABC=true and re
if factorize_ABC==true, it uses Aasen on the indefinite remaining system of blocks A, B, and C.

The most important routines of the model described in the QPModelBlockObject that are required here are (besides sizes and multiplications with the bundle matrix B)

QPModelBlockObject::add_BDBt() in forming the low rank Schur complement of H
QPModelBlockObject::add_localsys() in adding the barrier diagonal of the B block to the the Schur_complement
QPModelBlockObject::add_localrhs() for constructing the right hand side
QPModelBlockObject::computed_step() for communicating the solution step to the model

Member Function Documentation

◆ QPinit_KKTdata()

virtual int ConicBundle::QPDirectKKTSolver::QPinit_KKTdata	(	QPSolverProxObject *	Hp,
		QPModelBlockObject *	model,
		const CH_Matrix_Classes::Sparsemat *	A,
		const CH_Matrix_Classes::Indexmatrix *	eq_indices
	)

virtual

returns 1 if this class is not applicable in the current data situation, otherwise it stores the data pointers and these need to stay valid throught the use of the other routines but are not deleted here

Parameters

Hp	may not be be NULL
model	may be NULL
A	may be NULL
eq_indices	if not NULL these rows of A correspond to equations

Implements ConicBundle::QPKKTSolverObject.

Referenced by QPDirectKKTSolver().

The documentation for this class was generated from the following file:

QPDirectKKTSolver.hxx

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ QPinit_KKTdata()