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]

Classes
class	MatrixConstraints
	Matrix type for A_bar. More...

Public Types
enum	EInequalityPickPolicy

Public Types inherited from ConstrainedOptPack::QPSchurPack::Constraints
enum	EPickPolicy

Public member functions
	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, bounds_tol)
	<<std comp>="">> members for feasibility tolerance for the bound constriants. More...

	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, inequality_tol)
	<<std comp>="">> members for feasibility tolerance for the general inequality constraints. More...

	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, equality_tol)
	<<std comp>="">> members for feasibility tolerance for the general equality constriants. More...

	STANDARD_MEMBER_COMPOSITION_MEMBERS (EInequalityPickPolicy, inequality_pick_policy)
	<<std comp>="">> members for policy used to select a violated constraint. More...

	ConstraintsRelaxedStd ()
	Constructs to uninitialized. More...

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. More...

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. More...

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. More...

void	ignore (size_type j)

value_type	get_bnd (size_type j, EBounds bnd) const

Additional Inherited Members
Public Member Functions inherited from ConstrainedOptPack::QPSchurPack::Constraints
virtual	~Constraints ()

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 89 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

Member Enumeration Documentation

enum ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::EInequalityPickPolicy

Definition at line 224 of file ConstrainedOptPack_ConstraintsRelaxedStd.hpp.

Constructor & Destructor Documentation

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

Constructs to uninitialized.

Definition at line 102 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

Member Function Documentation

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		bounds_tol
	)

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

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		inequality_tol
	)

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

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		equality_tol
	)

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

ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	EInequalityPickPolicy	,
		inequality_pick_policy
	)

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

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 116 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

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

Definition at line 238 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

size_type ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::n ( ) const

virtual

Implements ConstrainedOptPack::QPSchurPack::Constraints.

Definition at line 245 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

size_type ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::m_breve ( ) const

virtual

Implements ConstrainedOptPack::QPSchurPack::Constraints.

Definition at line 250 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 255 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::pick_violated_policy ( EPickPolicy pick_policy )

virtual

Implements ConstrainedOptPack::QPSchurPack::Constraints.

Definition at line 260 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

Constraints::EPickPolicy ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::pick_violated_policy ( ) const

virtual

Implements ConstrainedOptPack::QPSchurPack::Constraints.

Definition at line 275 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 290 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.

void ConstrainedOptPack::QPSchurPack::ConstraintsRelaxedStd::ignore ( size_type j )

virtual

Implements ConstrainedOptPack::QPSchurPack::Constraints.

Definition at line 506 of file ConstrainedOptPack_ConstraintsRelaxedStd.cpp.