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

#include <ROL_Bounds.hpp>

Inheritance diagram for ROL::Bounds< Real >:

Classes
class	Active

class	LowerBinding

class	PruneBinding

class	UpperBinding

Public Member Functions
	Bounds (const Vector< Real > &x, bool isLower=true, Real scale=1, Real feasTol=1e-2)

	Bounds (const ROL::Ptr< Vector< Real >> &x_lo, const ROL::Ptr< Vector< Real >> &x_up, const Real scale=1, const Real feasTol=1e-2)

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...

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...

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...

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...

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...

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

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...

Public Member Functions inherited from ROL::BoundConstraint< Real >
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...

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
const ROL::Ptr< Vector< Real > >	x_lo_

const ROL::Ptr< Vector< Real > >	x_up_

const Real	scale_

const Real	feasTol_

ROL::Ptr< Vector< Real > >	mask_

Real	min_diff_

Elementwise::ReductionMin< Real >	minimum_

ROL::Bounds::PruneBinding	prune_

Detailed Description

template<class Real>
class ROL::Bounds< Real >

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

Definition at line 59 of file ROL_Bounds.hpp.

Constructor & Destructor Documentation

template<class Real>

ROL::Bounds< Real >::Bounds	(	const Vector< Real > &	x,
		bool	isLower = `true`,
		Real	scale = `1`,
		Real	feasTol = `1e-2`
	)

inline

Definition at line 111 of file ROL_Bounds.hpp.

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

template<class Real>

ROL::Bounds< Real >::Bounds	(	const ROL::Ptr< Vector< Real >> &	x_lo,
		const ROL::Ptr< Vector< Real >> &	x_up,
		const Real	scale = `1`,
		const Real	feasTol = `1e-2`
	)

inline

Definition at line 130 of file ROL_Bounds.hpp.

References ROL::Bounds< Real >::mask_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::minimum_, ROL::Bounds< Real >::x_lo_, and ROL::Bounds< Real >::x_up_.

Member Function Documentation

template<class Real>

virtual void ROL::Bounds< 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 146 of file ROL_Bounds.hpp.

References ROL::apply, ROL::Vector< Real >::applyBinary(), ROL::Bounds< Real >::x_lo_, and ROL::Bounds< Real >::x_up_.

template<class Real>

virtual void ROL::Bounds< 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 from ROL::BoundConstraint< Real >.

Definition at line 163 of file ROL_Bounds.hpp.

References ROL::apply, ROL::Vector< Real >::applyBinary(), ROL::Bounds< Real >::feasTol_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::x_lo_, and ROL::Bounds< Real >::x_up_.

template<class Real>

void ROL::Bounds< 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 from ROL::BoundConstraint< Real >.

Definition at line 209 of file ROL_Bounds.hpp.

References ROL::Vector< Real >::applyBinary(), ROL::Bounds< Real >::mask_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::scale_, and ROL::Bounds< Real >::x_up_.

template<class Real>

void ROL::Bounds< 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 from ROL::BoundConstraint< Real >.

Definition at line 221 of file ROL_Bounds.hpp.

References ROL::Vector< Real >::applyBinary(), ROL::Bounds< Real >::mask_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::prune_, ROL::Bounds< Real >::scale_, and ROL::Bounds< Real >::x_up_.

template<class Real>

void ROL::Bounds< 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 from ROL::BoundConstraint< Real >.

Definition at line 235 of file ROL_Bounds.hpp.

References ROL::Vector< Real >::applyBinary(), ROL::Bounds< Real >::mask_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::scale_, and ROL::Bounds< Real >::x_lo_.

template<class Real>

void ROL::Bounds< 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 \(\epsilon\).