ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd Class Reference

Constraints subclass that is used to represent generic varaible bounds, and general inequality and equality constraints. More...

#include <ConstrainedOptPack_ConstraintsRelaxedStd.hpp>

Inheritance diagram for ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd:

[legend]List of all members.


Public member functions
void	bounds_tol (const value_type &bounds_tol)
	<<std comp="">> members for feasibility tolerance for the bound constriants.
void	inequality_tol (const value_type &inequality_tol)
	<<std comp="">> members for feasibility tolerance for the general inequality constraints.
void	equality_tol (const value_type &equality_tol)
	<<std comp="">> members for feasibility tolerance for the general equality constriants.
void	inequality_pick_policy (const EInequalityPickPolicy &inequality_pick_policy)
	<<std comp="">> members for policy used to select a violated constraint.
	ConstraintsRelaxedStd ()
	Constructs to uninitialized.
void	initialize (const VectorSpace::space_ptr_t &space_d_eta, value_type etaL, const Vector dL, const Vector dU, const MatrixOp E, BLAS_Cpp::Transp trans_E, const Vector b, const Vector eL, const Vector eU, const MatrixOp F, BLAS_Cpp::Transp trans_F, const Vector f, size_type m_undecomp, const size_type j_f_undecomp[], VectorMutable *Ed, bool check_F=true, value_type bounds_tol=1e-10, value_type inequality_tol=1e-10, value_type equality_tol=1e-10)
	Initialize constriants.
const MatrixConstraints &	A_bar_relaxed () const

Overridden from Constraints
size_type	n () const

size_type	m_breve () const

const MatrixOp &	A_bar () const
	Represents the constraints matrix.
void	pick_violated_policy (EPickPolicy pick_policy)

EPickPolicy	pick_violated_policy () const

void	pick_violated (const DVectorSlice &x, size_type j_viol, value_type constr_val, value_type viol_bnd_val, value_type norm_2_constr, EBounds bnd, bool can_ignore) const
	Here the next violated constraint to add to the active set is selected.
void	ignore (size_type j)

value_type	get_bnd (size_type j, EBounds bnd) const

Public Types
enum	EInequalityPickPolicy
	More...

Detailed Description

Constraints subclass that is used to represent generic varaible bounds, and general inequality and equality constraints.

The generic constraints represented by this class are those of the QPSolverRelaxed interface which are:

  
  (1.2)               etaL <=  eta
  (1.3)               dL   <=  d                                 <= dU
  (1.4)               eL   <=  op(E)*d - b*eta                   <= eU
  (1.5)                        P_u'*op(F)*d + (1 - eta) * P_u'*f  = 0

These constraints are converted into the form:


       [   dL    ]     [ I                    ]              [   dU    ]
       [   etaL  ] <=  [                   1  ] * [  d  ] <= [   inf   ]
  (2)  [   eL    ]     [ op(E)            -b  ]   [ eta ]    [   eU    ]
       [ -P_u'*f ]     [ P_u'*op(F)   -P_u'*f ]              [ -P_u'*f ]
       \_________/     \______________________/   \_____/    \_________/
         cL_bar                 A_bar'               x          cU_bar

       =>

  (3)   [     xl     ]    [  I        ]          [     xu     ]
        [  cl_breve  ] <= [  A_breve' ] * x  <=  [  cu_breve  ]

       =>

  (4)	cl_bar <= A_bar'*x <= cu_bar

The main responsibilities of this class are to expose a MatrixOp object for A_bar shown in (2) and to pick violated constraints.

Definition at line 76 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

Member Enumeration Documentation

enum ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::EInequalityPickPolicy

Definition at line 211 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

Constructor & Destructor Documentation

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::ConstraintsRelaxedStd ( )

Constructs to uninitialized.

Definition at line 89 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

Member Function Documentation

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::bounds_tol ( const value_type & bounds_tol ) [inline]

<<std comp="">> members for feasibility tolerance for the bound constriants.

Definition at line 222 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::inequality_tol ( const value_type & inequality_tol ) [inline]

<<std comp="">> members for feasibility tolerance for the general inequality constraints.

Definition at line 226 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::equality_tol ( const value_type & equality_tol ) [inline]

<<std comp="">> members for feasibility tolerance for the general equality constriants.

Definition at line 230 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::inequality_pick_policy ( const EInequalityPickPolicy & inequality_pick_policy ) [inline]

<<std comp="">> members for policy used to select a violated constraint.

Definition at line 234 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::initialize ( const VectorSpace::space_ptr_t & space_d_eta,

value_type etaL,

const Vector * dL,

const Vector * dU,

const MatrixOp * E,

BLAS_Cpp::Transp trans_E,

const Vector * b,

const Vector * eL,

const Vector * eU,

const MatrixOp * F,

BLAS_Cpp::Transp trans_F,

const Vector * f,

size_type m_undecomp,

const size_type j_f_undecomp[],

VectorMutable * Ed,

bool check_F = true,

value_type bounds_tol = 1e-10,

value_type inequality_tol = 1e-10,

value_type equality_tol = 1e-10

)

Initialize constriants.
If there are no variable bounds then set:
void(dL) == void(dU) == NULL
If there are no general inequality constraints then set:
void(E) == void(b) == void(eL) == void(eU) == NULL
If there are no general equality constraints then set:
void(F) = void(f) == NULL
If check_F == false, then the equality constriants in op(F) will not be checked as violated constriants. This is to facilitate the addition of the equality constraints to the initial schur complement and therefore these constraints should never be violated (except for illconditioning). The tolerances below which a constriant will not be considered violated are given by bounds_tol, inequality_tol and equality_tol.
Here, Ed is updated (if Ed != NULL) within the function this->pick_violated}(...). This saves some computational work of having to compute op(E)*d again. To skip computing this value, just set Ed == NULL.
ToDo: Specify more concretely exactly what the criteria is for considering that a constraint is violated or in picking the most violated constraint.

Parameters:

m_undecomp [in] Number of undecomposed equality constraints.

j_f_undecomp [in] array (size m_undecomp) of indexes of constraints in op(F)*d + (1-eta)*f that are not decomposed and therefore should be considered when looking for violated constraints. This array is used to define the mapping matrix P_u. It is required that this be sorted and that: j_f_undecomp[k+1] >= j_f_undecomp[k], for k = 0...m_undecomp-2. If m_undecomp == f->size() then j_f_undecomp == NULL is allowed and the matrix P_u will be the identity matrix.

Definition at line 103 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

const ConstraintsRelaxedStd::MatrixConstraints & ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::A_bar_relaxed ( ) const

Definition at line 225 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

size_type ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::n ( ) const [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 232 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

size_type ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::m_breve ( ) const [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 237 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

const MatrixOp & ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::A_bar ( ) const [virtual]

Represents the constraints matrix.

A_bar = [ I 0 op(E') op(F')*P_u ] [ 0 1 -b' -f'*P_u ]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 242 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::pick_violated_policy ( EPickPolicy pick_policy ) [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 247 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

Constraints::EPickPolicy ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::pick_violated_policy ( ) const [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 262 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::pick_violated ( const DVectorSlice & x,

size_type * j_viol,

value_type * constr_val,

value_type * viol_bnd_val,

value_type * norm_2_constr,

EBounds * bnd,

bool * can_ignore

) const [virtual]

Here the next violated constraint to add to the active set is selected.
Violated constraints are selected to to add to the active set in the following order:

The equality constraints are added first, one at a time (if not already added as part of the warm start).

Add inequality constraints according according to the following options:

ADD_BOUNDS_THEN_MOST_VIOLATED_INEQUALITY Check the variable bounds first and add the most violated. If no variable bounds are violated by more than this->bounds_tol() then check for the most violated inequality constraint by computing r = op(E)*d+b*eta and add the most violated bound (eL, eU) if one exists.

ADD_BOUNDS_THEN_FIRST_VIOLATED_INEQUALITY Check the variable bounds first and add the most violated. If no variable bounds are violated by more than this->bounds_tol() then check for the first violated inequality constraint by computing e(j)'*(op(E)*d+b*eta) one or more constraints at a time. This option may be better if the cost of computing op(E)*d is significant.

ADD_MOST_VIOLATED_BOUNDS_AND_INEQUALITY Select the most violated constraint from the variable bounds and the general inequality constraints by computing r = op(E)*d+b*eta then add the most violated variable bound. This option is always the most expensive but may result in less QP iterations.

As a side effect, the vector pointed to by Ed which was passed to this->initialize(...) will be guarrenteed to be updated for the current op(E)*d, where d = x(1,nd), if any of the following is true:

j_viol == 0

this->pick_violated_policy() == ADD_MOST_VIOLATED_BOUNDS_AND_INEQUALITY

this->pick_violated_policy() == ADD_BOUNDS_THEN_MOST_VIOLATED_INEQUALITY && j_viol > this->n()

If none of the above criteria applies then the client can not assume that Ed was updated and therefore the client must compute this value on its own.
Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 277 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::ignore ( size_type j ) [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 493 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

value_type ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::get_bnd ( size_type j,

EBounds bnd

) const [virtual]

Implements ConstrainedOptPack::QPSchurPack::Constraints.
Definition at line 501 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

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

Generated on Thu Sep 18 12:34:18 2008 for ConstrainedOptPack: C++ Tools for Constrained (and Unconstrained) Optimization by

1.3.9.1

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd Class Reference

Public member functions

Overridden from Constraints

Public Types

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation