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	BuildC

class	isGreater

class	LowerBinding

class	PruneBinding

class	SetZeroEntry

class	UpperBinding

Public Member Functions
	Bounds (const Vector< Real > &x, bool isLower=true, Real scale=1, Real feasTol=std::sqrt(ROL_EPSILON< Real >()))

	Bounds (const Ptr< Vector< Real >> &x_lo, const Ptr< Vector< Real >> &x_up, const Real scale=1, const Real feasTol=std::sqrt(ROL_EPSILON< Real >()))

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

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

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

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

void	applyInverseScalingFunction (Vector< Real > &dv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g) const override
	Apply inverse scaling function. More...

void	applyScalingFunctionJacobian (Vector< Real > &dv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g) const override
	Apply scaling function Jacobian. More...

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

	BoundConstraint (void)

	BoundConstraint (const Vector< Real > &x)

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

virtual const Ptr< const Vector< Real > >	getUpperBound (void) const
	Return the ref count pointer to the upper bound vector. 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=Real(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 xeps=Real(0), Real geps=Real(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=Real(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=Real(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 xeps=Real(0), Real geps=Real(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 xeps=Real(0), Real geps=Real(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=Real(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 xeps=Real(0), Real geps=Real(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 Member Functions
void	buildScalingFunction (Vector< Real > &d, const Vector< Real > &x, const Vector< Real > &g) const

Private Attributes
const Real	scale_

const Real	feasTol_

Ptr< Vector< Real > >	mask_

Real	min_diff_

Elementwise::ReductionMin< Real >	minimum_

Elementwise::ReductionMax< Real >	maximum_

ROL::Bounds::isGreater	isGreater_

ROL::Bounds::PruneBinding	prune_

ROL::Bounds::BuildC	buildC_

ROL::Bounds::SetZeroEntry	setZeroEntry_

Additional Inherited Members
Protected Member Functions inherited from ROL::BoundConstraint< Real >
Real	computeInf (const Vector< Real > &x) const

Protected Attributes inherited from ROL::BoundConstraint< Real >
Ptr< Vector< Real > >	lower_

Ptr< Vector< Real > >	upper_

Detailed Description

template<typename 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<typename Real >

Bounds::Bounds	(	const Vector< Real > &	x,
		bool	isLower = `true`,
		Real	scale = `1`,
		Real	feasTol = `std::sqrt(ROL_EPSILON<Real>())`
	)

Definition at line 59 of file ROL_Bounds_Def.hpp.

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

template<typename Real >

Bounds::Bounds	(	const Ptr< Vector< Real >> &	x_lo,
		const Ptr< Vector< Real >> &	x_up,
		const Real	scale = `1`,
		const Real	feasTol = `std::sqrt(ROL_EPSILON<Real>())`
	)

Definition at line 76 of file ROL_Bounds_Def.hpp.

References ROL::BoundConstraint< Real >::lower_, ROL::Bounds< Real >::mask_, ROL::Bounds< Real >::min_diff_, ROL::Bounds< Real >::minimum_, and ROL::BoundConstraint< Real >::upper_.

Member Function Documentation

template<typename Real >

void Bounds::buildScalingFunction	(	Vector< Real > &	d,
		const Vector< Real > &	x,
		const Vector< Real > &	g
	)		const

private

Definition at line 229 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary(), ROL::Vector< Real >::axpy(), ROL::Vector< Real >::plus(), ROL::Vector< Real >::set(), ROL::Vector< Real >::setScalar(), and zero.

Referenced by ROL::Bounds< Real >::applyInverseScalingFunction(), and ROL::Bounds< Real >::applyScalingFunctionJacobian().

template<typename Real >

void Bounds::project ( Vector< Real > & x )

overridevirtual

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 91 of file ROL_Bounds_Def.hpp.

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

template<typename Real >

void Bounds::projectInterior ( Vector< Real > & x )

overridevirtual

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 109 of file ROL_Bounds_Def.hpp.

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

Referenced by testRandomInputs().

template<typename Real >

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

overridevirtual

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

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

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 156 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary().

template<typename Real >

void Bounds::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	xeps = `Real(0)`,
		Real	geps = `Real(0)`
	)

overridevirtual

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

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

Parameters

[out]	v	is the variable to be pruned.
[in]	g	is the negative search direction.
[in]	x	is the current optimization variable.
[in]	xeps	is the active-set tolerance \(\epsilon_x\).
[in]	geps	is the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 169 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary().

template<typename Real >

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

overridevirtual

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

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

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 184 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary().

template<typename Real >

void Bounds::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	g,
		const Vector< Real > &	x,
		Real	xeps = `Real(0)`,
		Real	geps = `Real(0)`
	)

overridevirtual

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

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

Parameters

[out]	v	is the variable to be pruned.
[in]	g	is the negative search direction.
[in]	x	is the current optimization variable.
[in]	xeps	is the active-set tolerance \(\epsilon_x\).
[in]	geps	is the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 197 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary().

template<typename Real >

bool Bounds::isFeasible ( const Vector< Real > & v )

overridevirtual

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 from ROL::BoundConstraint< Real >.

Definition at line 212 of file ROL_Bounds_Def.hpp.

template<typename Real >

void Bounds::applyInverseScalingFunction	(	Vector< Real > &	dv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		const Vector< Real > &	g
	)		const

overridevirtual

Apply inverse scaling function.

This function applies the inverse scaling function \(d(x,g)\) to a vector \(v\), i.e., the output is \(\mathrm{diag}(d(x,g)^{-1})v\). The scaling function must satisfy: (i) \(d(x,g)_i = 0\) if \(x_i = a_i\) and \(g_i \ge 0\); (ii) \(d(x,g)_i = 0\) if \(x_i = b_i\) and \(g_i \le 0\); and (iii) \(d(x,g)_i > 0\) otherwise.

Parameters

[out]	dv	is the inverse scaling function applied to v.
[in]	v	is the vector being scaled.
[in]	x	is the primal vector at which the scaling function is evaluated.
[in]	g	is the dual vector at which the scaling function is evaluated.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 289 of file ROL_Bounds_Def.hpp.

References ROL::Vector< Real >::applyBinary(), and ROL::Bounds< Real >::buildScalingFunction().

Referenced by testRandomInputs().

template<typename Real >

void Bounds::applyScalingFunctionJacobian	(	Vector< Real > &	dv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		const Vector< Real > &	g
	)		const

overridevirtual

Apply scaling function Jacobian.

This function applies the Jacobian of the scaling function \(d(x,g)\) to a vector \(v\). The output is \(\mathrm{diag}(d_x(x,g)g)v\). The scaling function must satisfy: (i) \(d(x,g)_i = 0\) if \(x_i = a_i\) and \(g_i \ge 0\); (ii) \(d(x,g)_i = 0\) if \(x_i = b_i\) and \(g_i \le 0\); and (iii) \(d(x,g)_i > 0\) otherwise.

Parameters

[out]	dv	is the scaling function Jacobian applied to v.
[in]	v	is the vector being scaled.
[in]	x	is the primal vector at which the scaling function is evaluated.
[in]	g	is the dual vector at which the scaling function is evaluated.