A BoundConstraint formed from a single bound constraint replacated according to a SampleGenerator. More...

#include <ROL_SimulatedBoundConstraint.hpp>

Inheritance diagram for ROL::SimulatedBoundConstraint< Real >:

Public Member Functions
	~SimulatedBoundConstraint ()

	SimulatedBoundConstraint (const Ptr< SampleGenerator< Real >> &sampler, const Ptr< BoundConstraint< Real >> &bnd)

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

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=Real(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 xeps=Real(0), Real geps=Real(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=Real(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 xeps=Real(0), Real geps=Real(0))
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...

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

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

bool	isFeasible (const Vector< Real > &v)
	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
	Apply inverse scaling function. More...

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

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

	BoundConstraint (void)

	BoundConstraint (const Vector< Real > &x)

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
const Vector< Real > &	getVector (const Vector< Real > &x, int k) const

Vector< Real > &	getVector (Vector< Real > &x, int k) const

Private Attributes
const Ptr< SampleGenerator < Real > >	sampler_

const Ptr< BoundConstraint < Real > >	bnd_

Ptr< Vector< Real > >	l_

Ptr< Vector< Real > >	u_

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::SimulatedBoundConstraint< Real >

A BoundConstraint formed from a single bound constraint replacated according to a SampleGenerator.

Definition at line 25 of file ROL_SimulatedBoundConstraint.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::SimulatedBoundConstraint< Real >::~SimulatedBoundConstraint ( )

inline

Definition at line 51 of file ROL_SimulatedBoundConstraint.hpp.

template<class Real >

ROL::SimulatedBoundConstraint< Real >::SimulatedBoundConstraint	(	const Ptr< SampleGenerator< Real >> &	sampler,
		const Ptr< BoundConstraint< Real >> &	bnd
	)

inline

Definition at line 53 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::l_, ROL::SimulatedBoundConstraint< Real >::sampler_, and ROL::SimulatedBoundConstraint< Real >::u_.

Member Function Documentation

template<class Real >

const Vector<Real>& ROL::SimulatedBoundConstraint< Real >::getVector	(	const Vector< Real > &	x,
		int	k
	)		const

inlineprivate

Definition at line 32 of file ROL_SimulatedBoundConstraint.hpp.

Referenced by ROL::SimulatedBoundConstraint< Real >::applyInverseScalingFunction(), ROL::SimulatedBoundConstraint< Real >::applyScalingFunctionJacobian(), ROL::SimulatedBoundConstraint< Real >::isFeasible(), ROL::SimulatedBoundConstraint< Real >::project(), ROL::SimulatedBoundConstraint< Real >::projectInterior(), ROL::SimulatedBoundConstraint< Real >::pruneLowerActive(), and ROL::SimulatedBoundConstraint< Real >::pruneUpperActive().

template<class Real >

Vector<Real>& ROL::SimulatedBoundConstraint< Real >::getVector	(	Vector< Real > &	x,
		int	k
	)		const

inlineprivate

Definition at line 41 of file ROL_SimulatedBoundConstraint.hpp.

template<class Real >

void ROL::SimulatedBoundConstraint< 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 68 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

void ROL::SimulatedBoundConstraint< 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 76 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

void ROL::SimulatedBoundConstraint< Real >::pruneUpperActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `Real(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

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

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 84 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

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

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

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 92 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

void ROL::SimulatedBoundConstraint< Real >::pruneLowerActive	(	Vector< Real > &	v,
		const Vector< Real > &	x,
		Real	eps = `Real(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

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

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 100 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

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

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

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 108 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

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

inlinevirtual

Return the ref count pointer to the lower bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 116 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::l_.

template<class Real >

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

inlinevirtual

Return the ref count pointer to the upper bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 120 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::u_.

template<class Real >

bool ROL::SimulatedBoundConstraint< 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 from ROL::BoundConstraint< Real >.

Definition at line 124 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

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

inlinevirtual

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 134 of file ROL_SimulatedBoundConstraint.hpp.

References ROL::SimulatedBoundConstraint< Real >::bnd_, ROL::SimulatedBoundConstraint< Real >::getVector(), and ROL::SimulatedBoundConstraint< Real >::sampler_.

template<class Real >

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

inlinevirtual

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.