ConstrainedOptPack::QPSchurInitKKTSystemHessianSuperBasic Class Reference

Implementation of initial KKT system for all variables initially fixed and free where #Ko = B_RR#. More...

#include <ConstrainedOptPack_QPSchurInitKKTSystemHessianSuperBasic.hpp>

Inheritance diagram for ConstrainedOptPack::QPSchurInitKKTSystemHessianSuperBasic:

Public Member Functions
void	initialize_kkt_system (const DVectorSlice &g, const MatrixOp &G, value_type etaL, const SpVectorSlice &dL, const SpVectorSlice &dU, const MatrixOp *F, BLAS_Cpp::Transp trans_F, const DVectorSlice *f, const DVectorSlice &d, const SpVectorSlice &nu, size_type *n_R, i_x_free_t *i_x_free, i_x_fixed_t *i_x_fixed, bnd_fixed_t *bnd_fixed, j_f_decomp_t *j_f_decomp, DVector *b_X, Ko_ptr_t *Ko, DVector *fo) const
	Initialize the KKT system where the variables are initiallly fixed and free and no constraints are in Ko. More...
Public Member Functions inherited from ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem
virtual	~InitKKTSystem ()
virtual void	initialize_kkt_system (const Vector &g, const MatrixOp &G, value_type etaL, const Vector *dL, const Vector *dU, const MatrixOp *F, BLAS_Cpp::Transp trans_F, const Vector *f, const Vector *d, const Vector *nu, size_type *n_R, i_x_free_t *i_x_free, i_x_fixed_t *i_x_fixed, bnd_fixed_t *bnd_fixed, j_f_decomp_t *j_f_decomp, DVector *b_X, Ko_ptr_t *Ko, DVector *fo) const =0
	Initializes the KKT system. More...

Additional Inherited Members
Public Types inherited from ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem
typedef std::vector< size_type >	i_x_free_t
typedef std::vector< size_type >	i_x_fixed_t
typedef std::vector< EBounds >	bnd_fixed_t
typedef std::vector< size_type >	j_f_decomp_t
typedef Teuchos::RCP< const MatrixSymOpNonsing >	Ko_ptr_t

Detailed Description

Implementation of initial KKT system for all variables initially fixed and free where #Ko = B_RR#.

In this implementation, #G# must support the {MatrixHessianSuperBasic} interface.

Definition at line 56 of file ConstrainedOptPack_QPSchurInitKKTSystemHessianSuperBasic.hpp.

Member Function Documentation

void ConstrainedOptPack::QPSchurInitKKTSystemHessianSuperBasic::initialize_kkt_system	(	const DVectorSlice &	g,
		const MatrixOp &	G,
		value_type	etaL,
		const SpVectorSlice &	dL,
		const SpVectorSlice &	dU,
		const MatrixOp *	F,
		BLAS_Cpp::Transp	trans_F,
		const DVectorSlice *	f,
		const DVectorSlice &	d,
		const SpVectorSlice &	nu,
		size_type *	n_R,
		i_x_free_t *	i_x_free,
		i_x_fixed_t *	i_x_fixed,
		bnd_fixed_t *	bnd_fixed,
		j_f_decomp_t *	j_f_decomp,
		DVector *	b_X,
		Ko_ptr_t *	Ko,
		DVector *	fo
	)		const

Initialize the KKT system where the variables are initiallly fixed and free and no constraints are in Ko.

The Hessian for the QP without the relaxation #G# is represented as a {MatrixHessianSuperBasic} object and is:

#G = Q_R*B_RR*Q_R' + Q_R*op(B_RX)*Q_X' + Q_X*op(B_RX')*Q_R + Q_X*B_XX*Q_X'#

If #G# does not support the interface #MatrixHessianSuperBasic# then an exception will be thrown.

Given the above parts of #G#, define: #[nd,nd_R] = size(G.Q_R)# and #[nd,nd_X] = size(G.Q_X)#. Then initial KKT system is defined as:

#n_R = nd_R#\ if #i_x_free.size() > 0# then #i_x_free[(G.Q_R.begin()+l-1)->col_j()-1] = (G.Q_R.begin()+l-1)->row_i(), l = 1...nd_R#\ if #i_x_free.size() == 0# then #i_x_free is implicitly identity#\ #i_x_fixed[(G.Q_X.begin()+l-1)->col_j()-1] = (G.Q_X.begin()+l-1)->row_i(), l = 1...nd_X#\ #i_x_fixed[nd_X] = nd+1#\ #bnd_fixed[l-1] = G.bnd_fixed[l-1], l = 1...nd_X#\ #bnd_fixed[nd_X] = LOWER#\ #j_f_decomp[] = empty#\ #b_X[l-1] = { dL(i) if bnd_fixed[l-1] == LOWER or EQUALITY, dU(i) if bnd_fixed[l-1] == UPPER }# #, l = 1...nd_X (where i = i_x_fixed[l-1])#\ #b_X[nd_X] = etaL#\ #Ko = G.B_RR#\ #fo = - G.Q_R'*g - op(G.B_RX)*b_X(1:nd_X)#\\

Above, it is assumed that if #G.bnd_fixed[l-1] == EQUALITY#, that #dL(G.i_x_fixed[l-1]) == dU(G.i_x_fixed[l-1]# but this may not be inforced by this class.

If the {MatrixHessianSuperBasic} interface is not suppored by #G# then a {QPSchurInitKKTSystemHessianFull} strategy object is used to try to initialize the KKT system.

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

• ConstrainedOptPack_QPSchurInitKKTSystemHessianSuperBasic.hpp