Require positivity of slack variables. More...

#include <ROL_InteriorPoint.hpp>

Inheritance diagram for ROL::InteriorPointBoundConstraint< Real >:

Public Member Functions
	InteriorPointBoundConstraint (const Vector< Real > &x)

void	project (Vector< Real > &x)
	Project optimization variables onto the bounds. More...

void	pruneUpperActive (Vector< Real > &v, const Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...

void	pruneUpperActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...

void	pruneLowerActive (Vector< Real > &v, const Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...

void	pruneLowerActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. More...

void	setVectorToUpperBound (Vector< Real > &u)
	Set the input vector to the upper bound. More...

void	setVectorToLowerBound (Vector< Real > &l)
	Set the input vector to the lower bound. More...

bool	isFeasible (const Vector< Real > &v)
	Check if the vector, v, is feasible. More...

Public Member Functions inherited from ROL::BoundConstraint< Real >
virtual	~BoundConstraint ()

	BoundConstraint (void)

	BoundConstraint (const Teuchos::RCP< Vector< Real > > &x_lo, const Teuchos::RCP< Vector< Real > > &x_up, Real scale=1.0)
	Default constructor. More...

virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update bounds. More...

virtual void	pruneActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...

virtual void	pruneActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...

void	activate (void)
	Turn on bounds. More...

void	deactivate (void)
	Turn off bounds. More...

bool	isActivated (void)
	Check if bounds are on. More...

void	pruneInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
	Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...

void	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)

void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)

void	pruneInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
	Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...

void	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)

void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)

void	computeProjectedGradient (Vector< Real > &g, const Vector< Real > &x)
	Compute projected gradient. More...

void	computeProjectedStep (Vector< Real > &v, const Vector< Real > &x)
	Compute projected step. More...

Private Types
typedef Vector< Real >	V

typedef PartitionedVector< Real >	PV

typedef PV::size_type	size_type

Private Attributes
Teuchos::RCP< BoundConstraint< Real > >	bc_

Teuchos::RCP< Vector< Real > >	lower_

Teuchos::RCP< Vector< Real > >	upper_

Static Private Attributes
static const size_type	OPT = 0

static const size_type	SLACK = 1

Detailed Description

template<class Real>
class ROL::InteriorPointBoundConstraint< Real >

Require positivity of slack variables.

Definition at line 352 of file ROL_InteriorPoint.hpp.

Member Typedef Documentation

template<class Real >

typedef Vector<Real> ROL::InteriorPointBoundConstraint< Real >::V

private

Definition at line 354 of file ROL_InteriorPoint.hpp.

template<class Real >

typedef PartitionedVector<Real> ROL::InteriorPointBoundConstraint< Real >::PV

private

Definition at line 355 of file ROL_InteriorPoint.hpp.

template<class Real >

typedef PV::size_type ROL::InteriorPointBoundConstraint< Real >::size_type

private

Definition at line 356 of file ROL_InteriorPoint.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::InteriorPointBoundConstraint< Real >::InteriorPointBoundConstraint ( const Vector< Real > & x )

inline

Definition at line 368 of file ROL_InteriorPoint.hpp.

References ROL::Vector< Real >::clone(), and ROL::PartitionedVector< Real >::get().

Member Function Documentation

template<class Real >

void ROL::InteriorPointBoundConstraint< Real >::project ( Vector< Real > & x )

inlinevirtual

Project optimization variables onto the bounds.

This function implements the projection of \(x\) onto the bounds, i.e.,

\[ (P_{[a,b]}(x))(\xi) = \min\{b(\xi),\max\{a(\xi),x(\xi)\}\} \quad \text{for almost every }\xi\in\Xi. \]

Parameters

[in,out] x is the optimization variable.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 395 of file ROL_InteriorPoint.hpp.

template<class Real >

void ROL::InteriorPointBoundConstraint< Real >::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps
	)

inlinevirtual

Set variables to zero if they correspond to the upper \(\epsilon\)-active set.

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-active set is defined as

\[ \mathcal{A}^+_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = b(\xi)-\epsilon\,\}. \]

Parameters

[out]	v	is the variable to be pruned.
[in]	x	is the current optimization variable.
[in]	eps	is the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 399 of file ROL_InteriorPoint.hpp.

template<class Real >

void ROL::InteriorPointBoundConstraint< Real >::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps
	)

inlinevirtual

Set variables to zero if they correspond to the upper \(\epsilon\)-binding set.

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-binding set is defined as

\[ \mathcal{B}^+_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = b(\xi)-\epsilon,\; g(\xi) < 0 \,\}. \]

Parameters

[out]	v	is the variable to be pruned.
[in]	x	is the current optimization variable.
[in]	g	is the negative search direction.
[in]	eps	is the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 403 of file ROL_InteriorPoint.hpp.

template<class Real >

void ROL::InteriorPointBoundConstraint< Real >::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps
	)

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-active set.

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-active set is defined as

\[ \mathcal{A}^-_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = a(\xi)+\epsilon\,\}. \]

Parameters

[out]	v	is the variable to be pruned.
[in]	x	is the current optimization variable.
[in]	eps	is the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 408 of file ROL_InteriorPoint.hpp.

template<class Real >

void ROL::InteriorPointBoundConstraint< Real >::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps
	)

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-binding set.

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-binding set is defined as

\[ \mathcal{B}^-_\epsilon(x) = \{\,\xi\in\Xi\,:\,x(\xi) = a(\xi)+\epsilon,\; g(\xi) > 0 \,\}. \]

Parameters

[out]	v	is the variable to be pruned.
[in]	x	is the current optimization variable.
[in]	g	is the negative search direction.
[in]	eps	is the active-set tolerance \(\epsilon\).