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ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem Class Reference

Interface for the object that forms the initial KKT system {abstract}. More...

#include <ConstrainedOptPack_QPSolverRelaxedQPSchur.hpp>

Inheritance diagram for ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem:
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Public Types

typedef std::vector< size_type > i_x_free_t
 
typedef std::vector< size_type > i_x_fixed_t
 
typedef std::vector< EBoundsbnd_fixed_t
 
typedef std::vector< size_type > j_f_decomp_t
 
typedef Teuchos::RCP< const
MatrixSymOpNonsing > 
Ko_ptr_t
 

Public Member Functions

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.

Detailed Description

Interface for the object that forms the initial KKT system {abstract}.

Note that this interface is set up such that the relaxation variable must always be initially fixed (and rightly so to avoid illconditioning).

Definition at line 71 of file ConstrainedOptPack_QPSolverRelaxedQPSchur.hpp.


Member Typedef Documentation


Constructor & Destructor Documentation

virtual ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem::~InitKKTSystem ( ) [inline, virtual]

Member Function Documentation

virtual void ConstrainedOptPack::QPSolverRelaxedQPSchur::InitKKTSystem::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 [pure virtual]

Initializes the KKT system.

Let the following permutation matrices define the selection of the initial KKT system:

Q = [ Q_R, Q_X ] : Initially fixed Q_R and free Q_X variables

P = [ P_d, P_u ] : Decomposed P_d and undecomposed P_u constraints

Given the definitions of Q and P above, this function will return the initial KKT system:


     Ko = [ Q_R'*G*Q_R         Q_R'*op(F')*P_d ]
          [ P_d'*op(F)*Q_R     0               ]

     fo = [ -Q_R'*g - Q_R'*G*Q_X*b_X    ]
          [ -P_d'f - P_d'*op(F)*Q_X*b_X ]

     b_X = ??? (see below)
     
Parameters:
g[in] See QPSolverRelaxed::solve_qp()
G[in] See QPSolverRelaxed::solve_qp()
dL[in] See QPSolverRelaxed::solve_qp()
dU[in] See QPSolverRelaxed::solve_qp()
F[in] See QPSolverRelaxed::solve_qp()
trans_f[in] See QPSolverRelaxed::solve_qp()
f[in] See QPSolverRelaxed::solve_qp()
d[in] See QPSolverRelaxed::solve_qp()
nu[in] See QPSolverRelaxed::solve_qp()
n_R[out] Number of initially free variables.
i_x_free[out] array (size n_R or 0): If i_x_free.size() > 0 then i_x_free[l-1], l = 1...n_R defines the matrix Q_R as:
Q_R(:,l) = e(i_x_free[l-1]), l = 1...n_R
If i_x_free.size() == 0 then i_x_free is implicitly identity and Q_R is defiend as:
Q_R(:,l) = e(l), l = 1...n_R
The ordering of these indices is significant.
i_x_fixed[out] array (size n_X): i_x_fixed[l-1], l = 1...n_X defines the matrix Q_X as:
Q_X(:,l) = e(i_x_fixed[l-1]), l = 1...n_X
The ordering of these indices is significant.
bnd_fixed[out] array (size n_X): bnd_fixed[l-1], l = 1...n_X defines the initial active set as:
                           / LOWER : b_X(l) = dL(i_x_fixed[l-1])
     bnd_fixed[l-1] = |  UPPER : b_X(l) = dU(i_x_fixed[l-1])
                       \ EQUALITY : b_X(l) = dL(i) = dU(i) (i = i_x_fixed[l-1])
     
j_f_decomp[out] array (size m): j_f_decomp[p-1], p = 1...m defines the decomposed equalities included in Ko as:
P_d(:,p) = e(j_f_decomp[p-1]), p = 1...m
The ordering of these indices is significant and are not necessarily sorted in assending or decending order.
b_X[out] vector (size n_X): Initial varaible bounds (see bnd_fixed above). Note that the relaxation variable is always one of the initially fixed variables.
Ko[in/out] Initial KKT matrix (size (n_R+m) x (n_R+m)). On output, Ko will contain a possibly dynamically allocated nonsingular matrix object that represents Ko. In input, if Ko->get() != NULL, and no other objects have a reference to this object (based on Ko->count(), and it is of the proper type, then this matrix may be reused.
fo[out] vector (size n_R + m) of the rhs for the initial KKT system.

Implemented in ConstrainedOptPack::QPSchurInitKKTSystemHessianFull.


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