#include <ROL_StdBoundConstraint.hpp>

Inheritance diagram for ROL::StdBoundConstraint< Real >:

Public Member Functions
	StdBoundConstraint (std::vector< Real > &x, bool isLower=false, Real scale=Real(1), const Real feasTol=std::sqrt(ROL_EPSILON< Real >()))

	StdBoundConstraint (std::vector< Real > &l, std::vector< Real > &u, Real scale=Real(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 > &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...

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...

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
Real	buildC (int i) const

Real	sgn (Real x) const

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

Private Attributes
int	dim_

std::vector< Real >	x_lo_

std::vector< Real >	x_up_

const Real	scale_

const Real	feasTol_

Real	min_diff_

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<class Real>
class ROL::StdBoundConstraint< Real >

Definition at line 58 of file ROL_StdBoundConstraint.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::StdBoundConstraint< Real >::StdBoundConstraint	(	std::vector< Real > &	x,
		bool	isLower = `false`,
		Real	scale = `Real(1)`,
		const Real	feasTol = `std::sqrt(ROL_EPSILON<Real>())`
	)

Definition at line 55 of file ROL_StdBoundConstraint_Def.hpp.

References ROL::BoundConstraint< Real >::activateLower(), ROL::BoundConstraint< Real >::activateUpper(), ROL::StdBoundConstraint< Real >::dim_, ROL::BoundConstraint< Real >::lower_, ROL::BoundConstraint< Real >::upper_, ROL::StdBoundConstraint< Real >::x_lo_, and ROL::StdBoundConstraint< Real >::x_up_.

template<class Real >

ROL::StdBoundConstraint< Real >::StdBoundConstraint	(	std::vector< Real > &	l,
		std::vector< Real > &	u,
		Real	scale = `Real(1)`,
		const Real	feasTol = `std::sqrt(ROL_EPSILON<Real>())`
	)

Definition at line 75 of file ROL_StdBoundConstraint_Def.hpp.

References ROL::BoundConstraint< Real >::activate(), ROL::StdBoundConstraint< Real >::dim_, ROL::BoundConstraint< Real >::lower_, ROL::StdBoundConstraint< Real >::min_diff_, ROL::BoundConstraint< Real >::upper_, ROL::StdBoundConstraint< Real >::x_lo_, and ROL::StdBoundConstraint< Real >::x_up_.

Member Function Documentation

template<class Real>

Real ROL::StdBoundConstraint< Real >::buildC ( int i ) const

inlineprivate

Definition at line 73 of file ROL_StdBoundConstraint.hpp.

References ROL::StdBoundConstraint< Real >::x_lo_, and ROL::StdBoundConstraint< Real >::x_up_.

template<class Real>

Real ROL::StdBoundConstraint< Real >::sgn ( Real x ) const

inlineprivate

Definition at line 78 of file ROL_StdBoundConstraint.hpp.

References zero.

template<class Real >

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

private

Definition at line 235 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 94 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 112 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 141 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 157 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 191 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 175 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

bool ROL::StdBoundConstraint< Real >::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 209 of file ROL_StdBoundConstraint_Def.hpp.

template<class Real >

void ROL::StdBoundConstraint< Real >::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 267 of file ROL_StdBoundConstraint_Def.hpp.

Referenced by testCases(), and testRandomInputs().

template<class Real >

void ROL::StdBoundConstraint< Real >::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.