Provides the interface to apply upper and lower bound constraints. More...

#include <ROL_BoundConstraint.hpp>

Inheritance diagram for ROL::BoundConstraint< Real >:

Public Member Functions
virtual	~BoundConstraint ()

	BoundConstraint (void)

	BoundConstraint (const Vector< Real > &x)

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

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

virtual void	projectInterior (Vector< Real > &x)
	Project optimization variables into the interior of the feasible set. More...

virtual void	pruneUpperActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...

virtual void	pruneUpperActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...

virtual void	pruneLowerActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...

virtual void	pruneLowerActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...

virtual const ROL::Ptr< const Vector< Real > >	getLowerBound (void) const
	Return the ref count pointer to the lower bound vector. More...

virtual const ROL::Ptr< const Vector< Real > >	getUpperBound (void) const
	Return the ref count pointer to the upper bound vector. More...

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

void	activateLower (void)
	Turn on lower bound. More...

void	activateUpper (void)
	Turn on upper bound. More...

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

void	deactivateLower (void)
	Turn off lower bound. More...

void	deactivateUpper (void)
	Turn off upper bound. More...

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

bool	isLowerActivated (void) const
	Check if lower bound are on. More...

bool	isUpperActivated (void) const
	Check if upper bound are on. More...

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

void	pruneActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...

void	pruneActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...

void	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...

void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...

void	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...

void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...

void	pruneInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...

void	pruneInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
	Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...

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 Attributes
bool	Lactivated_
	Flag that determines whether or not the lower bounds are being used. More...

bool	Uactivated_
	Flag that determines whether or not the upper bounds are being used. More...

Ptr< Vector< Real > >	lower_

Ptr< Vector< Real > >	upper_

bool	hasSetScalar_

Detailed Description

template<class Real>
class ROL::BoundConstraint< Real >

Provides the interface to apply upper and lower bound constraints.

ROL's bound constraint class is to designed to handle point wise bound constraints on optimization variables. That is, let \(\mathcal{X}\) be a Banach space of functions from \(\Xi\) into \(\mathbb{R}\) (for example, \(\Xi\subset\mathbb{R}^d\) for some positive integer \(d\) and \(\mathcal{X}=L^2(\Xi)\) or \(\Xi = \{1,\ldots,n\}\) and \(\mathcal{X}=\mathbb{R}^n\)). For any \(x\in\mathcal{X}\), we consider bounds of the form

\[ a(\xi) \le x(\xi) \le b(\xi) \quad \text{for almost every }\xi\in\Xi. \]

Here, \(a(\xi)\le b(\xi)\) for almost every \(\xi\in\Xi\) and \(a,b\in \mathcal{X}\).

Definition at line 72 of file ROL_BoundConstraint.hpp.

Constructor & Destructor Documentation

template<class Real>

virtual ROL::BoundConstraint< Real >::~BoundConstraint ( )

inlinevirtual

Definition at line 82 of file ROL_BoundConstraint.hpp.

template<class Real>

ROL::BoundConstraint< Real >::BoundConstraint ( void )

inline

Definition at line 84 of file ROL_BoundConstraint.hpp.

template<class Real>

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

inline

Definition at line 86 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::hasSetScalar_, ROL::BoundConstraint< Real >::lower_, and ROL::BoundConstraint< Real >::upper_.

Member Function Documentation

template<class Real>

virtual void ROL::BoundConstraint< Real >::update	(	const Vector< Real > &	x,
		bool	flag = `true`,
		int	iter = `-1`
	)

inlinevirtual

Update bounds.

The update function allows the user to update the bounds at each new iterations.

Parameters

[in]	x	is the optimization variable.
[in]	flag	is set to true if control is changed.
[in]	iter	is the outer algorithm iterations count.

Reimplemented in ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::BoundConstraint_SimOpt< Real >.

Definition at line 109 of file ROL_BoundConstraint.hpp.

Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().

template<class Real>

virtual void ROL::BoundConstraint< 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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, ROL::Bounds< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 119 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isActivated().

Referenced by ROL::LineSearchStep< Real >::compute(), ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::PrimalDualActiveSetStep< Real >::computeCriticalityMeasure(), ROL::TrustRegionStep< Real >::computeCriticalityMeasure(), ROL::AugmentedLagrangianStep< Real >::computeGradient(), ROL::BoundConstraint< Real >::computeProjectedStep(), ROL::FletcherStep< Real >::computeProjGradientNorm(), ROL::LineSearchStep< Real >::GradDotStep(), ROL::Step< Real >::initialize(), ROL::MoreauYosidaPenaltyStep< Real >::initialize(), ROL::AugmentedLagrangianStep< Real >::initialize(), ROL::PrimalDualActiveSetStep< Real >::initialize(), ROL::TrustRegionStep< Real >::initialize(), ROL::ProjectedNewtonStep< Real >::update(), ROL::TrustRegion< Real >::update(), ROL::ProjectedSecantStep< Real >::update(), ROL::ProjectedNewtonKrylovStep< Real >::update(), ROL::InteriorPointStep< Real >::update(), ROL::TrustRegionStep< Real >::update(), and ROL::LineSearch< Real >::updateIterate().

template<class Real>

virtual void ROL::BoundConstraint< Real >::projectInterior ( Vector< Real > & x )

inlinevirtual

Project optimization variables into the interior of the feasible set.

This function implements the projection of \(x\) into the interior of the feasible set, i.e.,

\[ (\bar{P}_{[a,b]}(x))(\xi) \in (a(\xi),b(\xi)) \quad \text{for almost every }\xi\in\Xi. \]

Parameters

[in,out] x is the optimization variable.

Reimplemented in ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, ROL::Bounds< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 135 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isActivated().

Referenced by ROL::InteriorPointStep< Real >::initialize(), and ROL::TrustRegionStep< Real >::initialize().

template<class Real>

virtual void ROL::BoundConstraint< Real >::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::Bounds< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 152 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isUpperActivated().

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint< Real >::pruneActive(), and ROL::BoundConstraint< Real >::pruneUpperInactive().

template<class Real>

virtual void ROL::BoundConstraint< Real >::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

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

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::StdBoundConstraint< Real >, ROL::Bounds< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 171 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isUpperActivated().

template<class Real>

virtual void ROL::BoundConstraint< Real >::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::Bounds< Real >, ROL::BoundConstraint_Partitioned< Real >, ROL::StdBoundConstraint< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 188 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isLowerActivated().

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint< Real >::pruneActive(), and ROL::BoundConstraint< Real >::pruneLowerInactive().

template<class Real>

virtual void ROL::BoundConstraint< Real >::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inlinevirtual

Set variables to zero if they correspond to the \(\epsilon\)-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]	g	is the negative search direction.
[in]	x	is the current optimization variable.
[in]	eps	is the active-set tolerance \(\epsilon\).

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::Bounds< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 207 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isLowerActivated().

template<class Real>

virtual const ROL::Ptr<const Vector<Real> > ROL::BoundConstraint< Real >::getLowerBound ( void ) const

inlinevirtual

Return the ref count pointer to the lower bound vector.

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::Bounds< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 217 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::hasSetScalar_, and ROL::BoundConstraint< Real >::lower_.

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint_Partitioned< Real >::getLowerBound(), ROL::LowerBoundToConstraint< Real >::LowerBoundToConstraint(), and ROL::RandomizeFeasibleVector().

template<class Real>

virtual const ROL::Ptr<const Vector<Real> > ROL::BoundConstraint< Real >::getUpperBound ( void ) const

inlinevirtual

Return the ref count pointer to the upper bound vector.

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::Bounds< Real >, ROL::StdBoundConstraint< Real >, ROL::BoundConstraint_Partitioned< Real >, and ROL::SimulatedBoundConstraint< Real >.

Definition at line 225 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::hasSetScalar_, and ROL::BoundConstraint< Real >::upper_.

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint_Partitioned< Real >::getUpperBound(), ROL::RandomizeFeasibleVector(), and ROL::UpperBoundToConstraint< Real >::UpperBoundToConstraint().

template<class Real>

virtual bool ROL::BoundConstraint< Real >::isFeasible ( const Vector< Real > & v )

inlinevirtual

Check if the vector, v, is feasible.

This function returns true if \(v = P_{[a,b]}(v)\).

Parameters

[in] v is the vector to be checked.

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::RiskBoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::Bounds< Real >, ROL::BoundConstraint_Partitioned< Real >, ROL::SimulatedBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 237 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isActivated().

Referenced by ROL::TrustRegion< Real >::update(), and ROL::PrimalDualActiveSetStep< Real >::update().

template<class Real>

void ROL::BoundConstraint< Real >::activateLower ( void )

inline

Turn on lower bound.

This function turns on lower bounds.

Definition at line 248 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Lactivated_.

Referenced by ROL::BoundConstraint< Real >::activate(), ROL::Bounds< Real >::Bounds(), and ROL::StdBoundConstraint< Real >::StdBoundConstraint().

template<class Real>

void ROL::BoundConstraint< Real >::activateUpper ( void )

inline

Turn on upper bound.

This function turns on upper bounds.

Definition at line 256 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Uactivated_.

Referenced by ROL::BoundConstraint< Real >::activate(), ROL::Bounds< Real >::Bounds(), and ROL::StdBoundConstraint< Real >::StdBoundConstraint().

template<class Real>

void ROL::BoundConstraint< Real >::activate ( void )

inline

Turn on bounds.

This function turns the bounds on.

Definition at line 264 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::activateLower(), and ROL::BoundConstraint< Real >::activateUpper().

Referenced by ROL::BoundConstraint_Partitioned< Real >::BoundConstraint_Partitioned(), ROL::BoundConstraint_SimOpt< Real >::BoundConstraint_SimOpt(), ROL::RiskBoundConstraint< Real >::RiskBoundConstraint(), and ROL::StdBoundConstraint< Real >::StdBoundConstraint().

template<class Real>

void ROL::BoundConstraint< Real >::deactivateLower ( void )

inline

Turn off lower bound.

This function turns the lower bounds off.

Definition at line 273 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Lactivated_.

Referenced by ROL::BoundConstraint< Real >::deactivate().

template<class Real>

void ROL::BoundConstraint< Real >::deactivateUpper ( void )

inline

Turn off upper bound.

This function turns the upper bounds off.

Definition at line 281 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Uactivated_.

Referenced by ROL::BoundConstraint< Real >::deactivate().

template<class Real>

void ROL::BoundConstraint< Real >::deactivate ( void )

inline

Turn off bounds.

This function turns the bounds off.

Definition at line 289 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::deactivateLower(), and ROL::BoundConstraint< Real >::deactivateUpper().

Referenced by ROL::BoundConstraint_Partitioned< Real >::BoundConstraint_Partitioned(), ROL::BoundConstraint_SimOpt< Real >::BoundConstraint_SimOpt(), ROL::RiskBoundConstraint< Real >::RiskBoundConstraint(), and ROL::Algorithm< Real >::run().

template<class Real>

bool ROL::BoundConstraint< Real >::isLowerActivated ( void ) const

inline

Check if lower bound are on.

This function returns true if the lower bounds are turned on.

Definition at line 298 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Lactivated_.

Referenced by ROL::BoundConstraint_Partitioned< Real >::BoundConstraint_Partitioned(), ROL::BoundConstraint< Real >::isActivated(), ROL::ObjectiveFromBoundConstraint< Real >::ObjectiveFromBoundConstraint(), ROL::BoundConstraint< Real >::pruneLowerActive(), and ROL::BoundConstraint< Real >::pruneLowerInactive().

template<class Real>

bool ROL::BoundConstraint< Real >::isUpperActivated ( void ) const

inline

Check if upper bound are on.

This function returns true if the upper bounds are turned on.

Definition at line 306 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::Uactivated_.

Referenced by ROL::BoundConstraint_Partitioned< Real >::BoundConstraint_Partitioned(), ROL::BoundConstraint< Real >::isActivated(), ROL::ObjectiveFromBoundConstraint< Real >::ObjectiveFromBoundConstraint(), ROL::BoundConstraint< Real >::pruneUpperActive(), and ROL::BoundConstraint< Real >::pruneUpperInactive().

template<class Real>

bool ROL::BoundConstraint< Real >::isActivated ( void ) const

inline

Check if bounds are on.

This function returns true if the bounds are turned on.

Definition at line 314 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isLowerActivated(), and ROL::BoundConstraint< Real >::isUpperActivated().

template<class Real>

void ROL::BoundConstraint< Real >::pruneActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

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

\[ \mathcal{A}_\epsilon(x) = \mathcal{A}^+_\epsilon(x)\cap\mathcal{A}^-_\epsilon(x). \]

Parameters

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

Definition at line 332 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isActivated(), ROL::BoundConstraint< Real >::pruneLowerActive(), and ROL::BoundConstraint< Real >::pruneUpperActive().

Referenced by ROL::ProjectedNewtonStep< Real >::compute(), ROL::ProjectedSecantStep< Real >::compute(), ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint< Real >::computeProjectedGradient(), ROL::LineSearchStep< Real >::GradDotStep(), ROL::BoundConstraint< Real >::pruneInactive(), ROL::LineSearch< Real >::status(), and ROL::TrustRegion< Real >::update().

template<class Real>

void ROL::BoundConstraint< Real >::pruneActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

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

\[ \mathcal{B}^+_\epsilon(x) = \mathcal{B}^+_\epsilon(x)\cap\mathcal{B}^-_\epsilon(x). \]

Parameters

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

Definition at line 351 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::isActivated(), ROL::BoundConstraint< Real >::pruneLowerActive(), and ROL::BoundConstraint< Real >::pruneUpperActive().

template<class Real>

void ROL::BoundConstraint< Real >::pruneLowerInactive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{A}_\epsilon(x)\). Here,

Parameters

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

Definition at line 365 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::isLowerActivated(), and ROL::BoundConstraint< Real >::pruneLowerActive().

template<class Real>

void ROL::BoundConstraint< Real >::pruneUpperInactive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{A}_\epsilon(x)\). Here,

Parameters

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

Definition at line 382 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::isUpperActivated(), and ROL::BoundConstraint< Real >::pruneUpperActive().

template<class Real>

void ROL::BoundConstraint< Real >::pruneLowerInactive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{B}_\epsilon(x)\).

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 \(\epsilon\).

Definition at line 400 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::isLowerActivated(), and ROL::BoundConstraint< Real >::pruneLowerActive().

template<class Real>

void ROL::BoundConstraint< Real >::pruneUpperInactive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{B}_\epsilon(x)\).

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 \(\epsilon\).

Definition at line 418 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::isUpperActivated(), and ROL::BoundConstraint< Real >::pruneUpperActive().

template<class Real>

void ROL::BoundConstraint< Real >::pruneInactive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{A}_\epsilon(x)\). Here,

Parameters

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

Definition at line 435 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::BoundConstraint< Real >::isActivated(), and ROL::BoundConstraint< Real >::pruneActive().

Referenced by ROL::ProjectedNewtonStep< Real >::compute(), ROL::ProjectedSecantStep< Real >::compute(), ROL::LineSearchStep< Real >::GradDotStep(), and ROL::LineSearch< Real >::status().

template<class Real>

void ROL::BoundConstraint< Real >::pruneInactive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	eps = `0`
	)

inline

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

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{B}_\epsilon(x)\).

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 \(\epsilon\).