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:

Inheritance graph
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List of all members.

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.

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 43 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.


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