Represents and manages the active set for the QPSchur algorithm. More...

#include <ConstrainedOptPack_QPSchur.hpp>

Public Types
typedef QPSchurPack::QP	QP

typedef MatrixSymAddDelUpdateable	MSADU

Public Member Functions
	STANDARD_COMPOSITION_MEMBERS (MatrixSymAddDelUpdateableWithOpNonsingular, schur_comp)
	�std comp� members for schur complement matrix S_hat. More...

	STANDARD_MEMBER_COMPOSITION_MEMBERS (MSADU::PivotTolerances, pivot_tols)
	Set the tolerances to use when updating the schur complement. More...

	ActiveSet (const schur_comp_ptr_t &schur_comp, MSADU::PivotTolerances pivot_tols=MSADU::PivotTolerances(1e-6, 1e-8, 1e-8))

Private Types
typedef std::vector< int >	ij_map_t

typedef std::map< int, size_type >	s_map_t

typedef std::vector< EBounds >	bnds_t

typedef std::vector< int >	l_fxfx_t

typedef std::vector< size_type >	P_row_t

typedef std::vector< size_type >	P_col_t

Private Member Functions
void	assert_initialized () const

void	assert_s (size_type s) const

void	reinitialize_matrices (bool test)

bool	remove_augmented_element (size_type sd, bool force_refactorization, MatrixSymAddDelUpdateable::EEigenValType eigen_val_drop, std::ostream *out, EOutputLevel output_level, bool allow_any_cond)

	ActiveSet ()

Private Attributes
bool	initialized_

bool	test_

QP *	qp_

const QP::x_init_t *	x_init_

size_type	n_

size_type	n_R_

size_type	m_

size_type	m_breve_

size_type	q_plus_hat_

size_type	q_F_hat_

size_type	q_C_hat_

ij_map_t	ij_map_

DVector	constr_norm_

bnds_t	bnds_

l_fxfx_t	l_fxfx_

U_hat_t	U_hat_

GenPermMatrixSlice	P_XF_hat_

P_row_t	P_XF_hat_row_

P_row_t	P_XF_hat_col_

GenPermMatrixSlice	P_FC_hat_

P_row_t	P_FC_hat_row_

P_row_t	P_FC_hat_col_

GenPermMatrixSlice	P_plus_hat_

P_row_t	P_plus_hat_row_

P_row_t	P_plus_hat_col_

GenPermMatrixSlice	Q_XD_hat_

P_row_t	Q_XD_hat_row_

P_row_t	Q_XD_hat_col_

DVector	d_hat_

DVector	z_hat_

DVector	p_z_hat_

DVector	mu_D_hat_

DVector	p_mu_D_hat_

Update the active set.
void	initialize (QP &qp, size_type num_act_change, const int ij_act_change[], const EBounds bnds[], bool test, bool salvage_init_schur_comp, std::ostream *out, EOutputLevel output_level)
	Initialize with an additional active set. More...

void	refactorize_schur_comp ()
	Reinitialize the schur complement factorization for the current active set. More...

bool	add_constraint (size_type ja, EBounds bnd_ja, bool update_steps, std::ostream *out, EOutputLevel output_level, bool force_refactorization=true, bool allow_any_cond=false)
	Add a constraint to the active set then refactorize the schur complemnt (if forced). More...

bool	drop_constraint (int jd, std::ostream *out, EOutputLevel output_level, bool force_refactorization=true, bool allow_any_cond=false)
	Drop a constraint from the active set then refactorize the schur complement (if forced). More...

bool	drop_add_constraints (int jd, size_type ja, EBounds bnd_ja, bool update_steps, std::ostream *out, EOutputLevel output_level)
	Drop a constraint from, then add a constraint to the active set and refactorize the schur complement. More...

access the QP
QP &	qp ()

const QP &	qp () const

Access the active sets quantities.
size_type	q_hat () const
	Return the total size of the schur complement. More...

size_type	q_plus_hat () const
	Return the number of constraints from A_bar added to the active set. More...

size_type	q_F_hat () const
	Return the number of variables that where initially fixed but are currently free or fixed to another bound. More...

size_type	q_C_hat () const
	Return the number of variables that where initially fixed but are currently fixed to another bound. More...

size_type	q_D_hat () const
	Return the number of variables that where initially fixed and are still currently fixed to their intial bounds. More...

int	ij_map (size_type s) const
	Returns -i for row & column of S_bar for an initially fixed variable left out of Ko that became free and returns j for the constraint a(j)'*x that was added to the active set. More...

size_type	s_map (int ij) const
	Map from a constraint or initially fixed variable to a row and column in the schur complement S_bar. More...

value_type	constr_norm (size_type s) const
	Returns \|\|a(j)\|\|2 where j = ij_map(s). More...

EBounds	bnd (size_type s) const
	Return which bound is active for the active constraint. More...

size_type	l_fxfx (size_type k) const
	Returns the indice of x_X(l) of the initially fixed variables that are still fixed at their original bounds. More...

const U_hat_t &	U_hat () const

const MatrixSymOpNonsing &	S_hat () const

const GenPermMatrixSlice &	P_XF_hat () const

const GenPermMatrixSlice &	P_FC_hat () const

const GenPermMatrixSlice &	P_plus_hat () const

const GenPermMatrixSlice &	Q_XD_hat () const

const DVectorSlice	d_hat () const

DVectorSlice	z_hat ()

const DVectorSlice	z_hat () const

DVectorSlice	p_z_hat ()

const DVectorSlice	p_z_hat () const

DVectorSlice	mu_D_hat ()

const DVectorSlice	mu_D_hat () const

DVectorSlice	p_mu_D_hat ()

const DVectorSlice	p_mu_D_hat () const

bool	is_init_fixed (size_type j) const
	Determine if a constriant was an initially fixed variable. More...

bool	all_dof_used_up () const
	Returns true if all the degrees of freedom of the QP are used up. More...

Detailed Description

Represents and manages the active set for the QPSchur algorithm.

This is a concrete type that encapsulates the maintaince of the active set and abstracts quantities associated with it.

At each iteration the dual active-set QP algorithm must solve the system:

 [ Ko       U_hat ]   [    v  ]   [  fo   ]
 [ U_hat'   V_hat ] * [ z_hat ] = [ d_hat ]

Above, U_hat contains the updates to the KKT system for adding constraints to the active set and freeing variables that where initially fixed and therefore left out of Ko.

This object maintains references to objects that represent the current augmented KKT system:

MatrixOp                      : U_hat        <: R^((n_R+m) x q_hat)
MatrixSymOp                   : V_hat        <: R^(q_hat x q_hat)
MatrixSymOpNonsing        : S_hat        <: R^(q_hat x q_hat)
GenPermMatrixSlice                : P_XF_hat     <: R^(n x q_hat)             (q_F_hat nonzeros)
GenPermMatrixSlice                : P_FC_hat     <: R^(q_hat x q_hat)         (q_C_hat nonzeros)
GenPermMatrixSlice                : P_plus_hat   <: R^((n+m_breve) x q_hat)   (q_plus_hat nonzeros)
GenPermMatrixSlice                : Q_XD_hat     <: R^(n x q_D_hat)           (q_D_hat nonzeros)
DVector                            : d_hat        <: R^(q_hat)
DVector                            : z_hat        <: R^(q_hat)

Definition at line 727 of file ConstrainedOptPack_QPSchur.hpp.

Member Typedef Documentation

typedef QPSchurPack::QP ConstrainedOptPack::QPSchur::ActiveSet::QP

Definition at line 734 of file ConstrainedOptPack_QPSchur.hpp.

typedef MatrixSymAddDelUpdateable ConstrainedOptPack::QPSchur::ActiveSet::MSADU

Definition at line 736 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::vector<int> ConstrainedOptPack::QPSchur::ActiveSet::ij_map_t

private

Definition at line 965 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::map<int,size_type> ConstrainedOptPack::QPSchur::ActiveSet::s_map_t

private

Definition at line 967 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::vector<EBounds> ConstrainedOptPack::QPSchur::ActiveSet::bnds_t

private

Definition at line 969 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::vector<int> ConstrainedOptPack::QPSchur::ActiveSet::l_fxfx_t

private

Definition at line 971 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::vector<size_type> ConstrainedOptPack::QPSchur::ActiveSet::P_row_t

private

Definition at line 973 of file ConstrainedOptPack_QPSchur.hpp.

typedef std::vector<size_type> ConstrainedOptPack::QPSchur::ActiveSet::P_col_t

private

Definition at line 975 of file ConstrainedOptPack_QPSchur.hpp.

Constructor & Destructor Documentation

ConstrainedOptPack::QPSchur::ActiveSet::ActiveSet	(	const schur_comp_ptr_t &	schur_comp,
		MSADU::PivotTolerances	pivot_tols = `MSADU::PivotTolerances( 1e-6,1e-8,1e-8 )`
	)

Definition at line 1021 of file ConstrainedOptPack_QPSchur.cpp.

ConstrainedOptPack::QPSchur::ActiveSet::ActiveSet ( )

private

Member Function Documentation

ConstrainedOptPack::QPSchur::ActiveSet::STANDARD_COMPOSITION_MEMBERS	(	MatrixSymAddDelUpdateableWithOpNonsingular	,
		schur_comp
	)

�std comp� members for schur complement matrix S_hat.

Warning: Resetting schur_comp will cause a reinitialization to an empty active set.

ConstrainedOptPack::QPSchur::ActiveSet::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	MSADU::PivotTolerances	,
		pivot_tols
	)

Set the tolerances to use when updating the schur complement.

void ConstrainedOptPack::QPSchur::ActiveSet::initialize	(	QP &	qp,
		size_type	num_act_change,
		const int	ij_act_change[],
		const EBounds	bnds[],
		bool	test,
		bool	salvage_init_schur_comp,
		std::ostream *	out,
		EOutputLevel	output_level
	)

Initialize with an additional active set.

If the initial schur complement is not full rank then an LDConstraintException exception will be thrown. The active set will contain all of the constraints it can such that the schur complement is nonsingular.

Definition at line 1039 of file ConstrainedOptPack_QPSchur.cpp.

void ConstrainedOptPack::QPSchur::ActiveSet::refactorize_schur_comp ( )

Reinitialize the schur complement factorization for the current active set.

ToDo: Finish documentation

Definition at line 1471 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::add_constraint	(	size_type	ja,
		EBounds	bnd_ja,
		bool	update_steps,
		std::ostream *	out,
		EOutputLevel	output_level,
		bool	force_refactorization = `true`,
		bool	allow_any_cond = `false`
	)

Add a constraint to the active set then refactorize the schur complemnt (if forced).

ToDo: Finish documentation

If the new KKT system is singular then the exeption MatrixSymAddDelUpdateable::SingularUpdateException will be thrown but the old KKT system will be kept intact.

If the reduced Hessian for the new KKT system does not have the correct inertia then the exception MatrixSymAddDelUpdateable::WrongInertiaUpdateException will be thrown but the old KKT system will be kept intact.

Returns: Returns true if any output was sent to *out.

Definition at line 1477 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::drop_constraint	(	int	jd,
		std::ostream *	out,
		EOutputLevel	output_level,
		bool	force_refactorization = `true`,
		bool	allow_any_cond = `false`
	)

Drop a constraint from the active set then refactorize the schur complement (if forced).

ToDo: Finish documentation

Returns true if any output was sent to *out.

Definition at line 1716 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::drop_add_constraints	(	int	jd,
		size_type	ja,
		EBounds	bnd_ja,
		bool	update_steps,
		std::ostream *	out,
		EOutputLevel	output_level
	)

Drop a constraint from, then add a constraint to the active set and refactorize the schur complement.

ToDo: Finish documentation

Returns true if any output was sent to *out.

Definition at line 1940 of file ConstrainedOptPack_QPSchur.cpp.

QPSchur::ActiveSet::QP & ConstrainedOptPack::QPSchur::ActiveSet::qp ( )

Definition at line 1954 of file ConstrainedOptPack_QPSchur.cpp.

const QPSchur::ActiveSet::QP & ConstrainedOptPack::QPSchur::ActiveSet::qp ( ) const

Definition at line 1961 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::q_hat ( ) const

Return the total size of the schur complement.

q_hat = q_plus_hat + q_F_hat + q_C_hat.

Definition at line 1967 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::q_plus_hat ( ) const

Return the number of constraints from A_bar added to the active set.

Definition at line 1973 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::q_F_hat ( ) const

Return the number of variables that where initially fixed but are currently free or fixed to another bound.

Definition at line 1979 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::q_C_hat ( ) const

Return the number of variables that where initially fixed but are currently fixed to another bound.

Definition at line 1985 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::q_D_hat ( ) const

Return the number of variables that where initially fixed and are still currently fixed to their intial bounds.

Definition at line 1991 of file ConstrainedOptPack_QPSchur.cpp.

int ConstrainedOptPack::QPSchur::ActiveSet::ij_map ( size_type s ) const

Returns -i for row & column of S_bar for an initially fixed variable left out of Ko that became free and returns j for the constraint a(j)'*x that was added to the active set.

1 <= s <= q_hat

Definition at line 1997 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::s_map ( int ij ) const

Map from a constraint or initially fixed variable to a row and column in the schur complement S_bar.

To determine if an initially fixed variable x(i) is now free call s_map(-i). If s_map(-i) returns zero then x(i) is still fixed. Otherwise s_map(-i) returns the row and column in S_bar for this change in the active set.

To determine if a constraint a(j)'*x is part of the active set call s_map(j). If s_map(j) returns zero then a(j)'*x is not part of the active set. Otherwise s_map(j) returns the row and column in S_bar for this change in the active set.

Definition at line 2003 of file ConstrainedOptPack_QPSchur.cpp.

value_type ConstrainedOptPack::QPSchur::ActiveSet::constr_norm ( size_type s ) const

Returns ||a(j)||2 where j = ij_map(s).

If ij_map(s) < 0, the this function returns zero.

1 <= s <= q_hat

Definition at line 2012 of file ConstrainedOptPack_QPSchur.cpp.

EBounds ConstrainedOptPack::QPSchur::ActiveSet::bnd ( size_type s ) const

Return which bound is active for the active constraint.

Definition at line 2018 of file ConstrainedOptPack_QPSchur.cpp.

size_type ConstrainedOptPack::QPSchur::ActiveSet::l_fxfx ( size_type k ) const

Returns the indice of x_X(l) of the initially fixed variables that are still fixed at their original bounds.

i <= k <= q_D_hat

Definition at line 2024 of file ConstrainedOptPack_QPSchur.cpp.

const QPSchur::U_hat_t & ConstrainedOptPack::QPSchur::ActiveSet::U_hat ( ) const

Definition at line 2030 of file ConstrainedOptPack_QPSchur.cpp.

const MatrixSymOpNonsing & ConstrainedOptPack::QPSchur::ActiveSet::S_hat ( ) const

Definition at line 2036 of file ConstrainedOptPack_QPSchur.cpp.

const GenPermMatrixSlice & ConstrainedOptPack::QPSchur::ActiveSet::P_XF_hat ( ) const

Definition at line 2042 of file ConstrainedOptPack_QPSchur.cpp.

const GenPermMatrixSlice & ConstrainedOptPack::QPSchur::ActiveSet::P_FC_hat ( ) const

Definition at line 2048 of file ConstrainedOptPack_QPSchur.cpp.

const GenPermMatrixSlice & ConstrainedOptPack::QPSchur::ActiveSet::P_plus_hat ( ) const

Definition at line 2054 of file ConstrainedOptPack_QPSchur.cpp.

const GenPermMatrixSlice & ConstrainedOptPack::QPSchur::ActiveSet::Q_XD_hat ( ) const

Definition at line 2060 of file ConstrainedOptPack_QPSchur.cpp.

const DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::d_hat ( ) const

Definition at line 2066 of file ConstrainedOptPack_QPSchur.cpp.

DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::z_hat ( )

Definition at line 2072 of file ConstrainedOptPack_QPSchur.cpp.

const DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::z_hat ( ) const

Definition at line 2078 of file ConstrainedOptPack_QPSchur.cpp.

DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::p_z_hat ( )

Definition at line 2084 of file ConstrainedOptPack_QPSchur.cpp.

const DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::p_z_hat ( ) const

Definition at line 2090 of file ConstrainedOptPack_QPSchur.cpp.

DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::mu_D_hat ( )

Definition at line 2096 of file ConstrainedOptPack_QPSchur.cpp.

const DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::mu_D_hat ( ) const

Definition at line 2102 of file ConstrainedOptPack_QPSchur.cpp.

DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::p_mu_D_hat ( )

Definition at line 2108 of file ConstrainedOptPack_QPSchur.cpp.

const DVectorSlice ConstrainedOptPack::QPSchur::ActiveSet::p_mu_D_hat ( ) const

Definition at line 2114 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::is_init_fixed ( size_type j ) const

Determine if a constriant was an initially fixed variable.

This function will return true if:

j <= n && x_init(j) != FREE

This is just a function of convienience

Definition at line 2120 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::all_dof_used_up ( ) const

Returns true if all the degrees of freedom of the QP are used up.

Definition at line 2126 of file ConstrainedOptPack_QPSchur.cpp.

void ConstrainedOptPack::QPSchur::ActiveSet::assert_initialized ( ) const

private

Definition at line 2133 of file ConstrainedOptPack_QPSchur.cpp.

void ConstrainedOptPack::QPSchur::ActiveSet::assert_s ( size_type s ) const

private

Definition at line 2141 of file ConstrainedOptPack_QPSchur.cpp.

void ConstrainedOptPack::QPSchur::ActiveSet::reinitialize_matrices ( bool test )

private

Definition at line 2146 of file ConstrainedOptPack_QPSchur.cpp.

bool ConstrainedOptPack::QPSchur::ActiveSet::remove_augmented_element	(	size_type	sd,
		bool	force_refactorization,
		MatrixSymAddDelUpdateable::EEigenValType	eigen_val_drop,
		std::ostream *	out,
		EOutputLevel	output_level,
		bool	allow_any_cond
	)