H1BoundConstraint< Real > Class Template Reference

#include <example_04.hpp>

Inheritance diagram for H1BoundConstraint< Real >:

Public Member Functions
	H1BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const Teuchos::RCP< BurgersFEM< Real > > &fem, Real scale=1.0)
bool	isFeasible (const ROL::Vector< Real > &x)
	Check if the vector, v, is feasible. More...
void	project (ROL::Vector< Real > &x)
	Project optimization variables onto the bounds. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
void	setVectorToUpperBound (ROL::Vector< Real > &u)
	Set the input vector to the upper bound. More...
void	setVectorToLowerBound (ROL::Vector< Real > &l)
	Set the input vector to the lower bound. More...
	H1BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const Teuchos::RCP< BurgersFEM< Real > > &fem, Real scale=1.0)
bool	isFeasible (const ROL::Vector< Real > &x)
	Check if the vector, v, is feasible. More...
void	project (ROL::Vector< Real > &x)
	Project optimization variables onto the bounds. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
void	setVectorToUpperBound (ROL::Vector< Real > &u)
	Set the input vector to the upper bound. More...
void	setVectorToLowerBound (ROL::Vector< Real > &l)
	Set the input vector to the lower bound. More...
	H1BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const Teuchos::RCP< BurgersFEM< Real > > &fem, Real scale=1.0)
bool	isFeasible (const ROL::Vector< Real > &x)
	Check if the vector, v, is feasible. More...
void	project (ROL::Vector< Real > &x)
	Project optimization variables onto the bounds. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
void	setVectorToUpperBound (ROL::Vector< Real > &u)
	Set the input vector to the upper bound. More...
void	setVectorToLowerBound (ROL::Vector< Real > &l)
	Set the input vector to the lower bound. More...
	H1BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const Teuchos::RCP< BurgersFEM< Real > > &fem, Real scale=1.0)
bool	isFeasible (const ROL::Vector< Real > &x)
	Check if the vector, v, is feasible. More...
void	project (ROL::Vector< Real > &x)
	Project optimization variables onto the bounds. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
void	pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. More...
void	pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
void	pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real eps)
	Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
void	setVectorToUpperBound (ROL::Vector< Real > &u)
	Set the input vector to the upper bound. More...
void	setVectorToLowerBound (ROL::Vector< Real > &l)
	Set the input vector to the lower bound. More...
Public Member Functions inherited from ROL::BoundConstraint< Real >
virtual	~BoundConstraint ()
	BoundConstraint (void)
	BoundConstraint (const Vector< Real > &x)
	BoundConstraint (const Teuchos::RCP< Vector< Real > > &x_lo, const Teuchos::RCP< Vector< Real > > &x_up, const Real scale=1)
	Default constructor. More...
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update bounds. More...
virtual const Teuchos::RCP< const Vector< Real > >	getLowerVectorRCP (void) const
	Return the ref count pointer to the lower bound vector. More...
virtual const Teuchos::RCP< const Vector< Real > >	getUpperVectorRCP (void) const
	Return the ref count pointer to the upper bound vector. More...
virtual const Teuchos::RCP< Vector< Real > >	getLowerVectorRCP (void)
	Return the ref count pointer to the lower bound vector. More...
virtual const Teuchos::RCP< Vector< Real > >	getUpperVectorRCP (void)
	Return the ref count pointer to the upper bound vector. More...
void	activate (void)
	Turn on bounds. More...
void	deactivate (void)
	Turn off bounds. More...
bool	isActivated (void)
	Check if bounds are on. 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	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0)
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	pruneLowerInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
void	pruneUpperInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0)
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	cast_vector (Teuchos::RCP< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
void	cast_const_vector (Teuchos::RCP< const std::vector< Real > > &xvec, const ROL::Vector< Real > &x) const
void	axpy (std::vector< Real > &out, const Real a, const std::vector< Real > &x, const std::vector< Real > &y) const
void	projection (std::vector< Real > &x)
void	cast_vector (Teuchos::RCP< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
void	cast_const_vector (Teuchos::RCP< const std::vector< Real > > &xvec, const ROL::Vector< Real > &x) const
void	axpy (std::vector< Real > &out, const Real a, const std::vector< Real > &x, const std::vector< Real > &y) const
void	projection (std::vector< Real > &x)
void	cast_vector (Teuchos::RCP< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
void	cast_const_vector (Teuchos::RCP< const std::vector< Real > > &xvec, const ROL::Vector< Real > &x) const
void	axpy (std::vector< Real > &out, const Real a, const std::vector< Real > &x, const std::vector< Real > &y) const
void	projection (std::vector< Real > &x)
void	cast_vector (Teuchos::RCP< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
void	cast_const_vector (Teuchos::RCP< const std::vector< Real > > &xvec, const ROL::Vector< Real > &x) const
void	axpy (std::vector< Real > &out, const Real a, const std::vector< Real > &x, const std::vector< Real > &y) const
void	projection (std::vector< Real > &x)

Private Attributes
int	dim_
std::vector< Real >	x_lo_
std::vector< Real >	x_up_
Real	min_diff_
Real	scale_
Teuchos::RCP< BurgersFEM< Real > >	fem_

Detailed Description

template<class Real>
class H1BoundConstraint< Real >

Definition at line 1316 of file example_04.hpp.

Constructor & Destructor Documentation

H1BoundConstraint() [1/4]

template<class Real >

H1BoundConstraint< Real >::H1BoundConstraint ( std::vector< Real > &  l, std::vector< Real > &  u, const Teuchos::RCP< BurgersFEM< Real > > &  fem, Real  scale = 1.0  )

inline

Definition at line 1364 of file example_04.hpp.

H1BoundConstraint() [2/4]

template<class Real >

H1BoundConstraint< Real >::H1BoundConstraint ( std::vector< Real > &  l, std::vector< Real > &  u, const Teuchos::RCP< BurgersFEM< Real > > &  fem, Real  scale = 1.0  )

inline

Definition at line 1423 of file example_06.hpp.

H1BoundConstraint() [3/4]

template<class Real >

H1BoundConstraint< Real >::H1BoundConstraint ( std::vector< Real > &  l, std::vector< Real > &  u, const Teuchos::RCP< BurgersFEM< Real > > &  fem, Real  scale = 1.0  )

inline

Definition at line 1441 of file example_07.hpp.

H1BoundConstraint() [4/4]

template<class Real >

H1BoundConstraint< Real >::H1BoundConstraint ( std::vector< Real > &  l, std::vector< Real > &  u, const Teuchos::RCP< BurgersFEM< Real > > &  fem, Real  scale = 1.0  )

inline

Definition at line 1423 of file example_08.hpp.

Member Function Documentation

cast_vector() [1/4]

template<class Real >

void H1BoundConstraint< Real >::cast_vector ( Teuchos::RCP< std::vector< Real > > &  xvec, ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1325 of file example_04.hpp.

cast_const_vector() [1/4]

template<class Real >

void H1BoundConstraint< Real >::cast_const_vector ( Teuchos::RCP< const std::vector< Real > > &  xvec, const ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1337 of file example_04.hpp.

axpy() [1/4]

template<class Real >

void H1BoundConstraint< Real >::axpy ( std::vector< Real > &  out, const Real  a, const std::vector< Real > &  x, const std::vector< Real > &  y  ) const

inlineprivate

Definition at line 1349 of file example_04.hpp.

projection() [1/4]

template<class Real >

void H1BoundConstraint< Real >::projection ( std::vector< Real > &  x )

inlineprivate

Definition at line 1357 of file example_04.hpp.

isFeasible() [1/4]

template<class Real >

bool H1BoundConstraint< Real >::isFeasible ( const ROL::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 1379 of file example_04.hpp.

project() [1/4]

template<class Real >

void H1BoundConstraint< Real >::project ( ROL::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 1391 of file example_04.hpp.

pruneLowerActive() [1/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1396 of file example_04.hpp.

pruneUpperActive() [1/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1407 of file example_04.hpp.

pruneActive() [1/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1418 of file example_04.hpp.

pruneLowerActive() [2/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-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 from ROL::BoundConstraint< Real >.

Definition at line 1430 of file example_04.hpp.

pruneUpperActive() [2/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 1442 of file example_04.hpp.

pruneActive() [2/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 \(\epsilon\)-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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1454 of file example_04.hpp.

setVectorToUpperBound() [1/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToUpperBound ( ROL::Vector< Real > &  u )

inlinevirtual

Set the input vector to the upper bound.

This function sets the input vector \(u\) to the upper bound \(b\).

Parameters

[out]

u

is the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1467 of file example_04.hpp.

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

setVectorToLowerBound() [1/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToLowerBound ( ROL::Vector< Real > &  l )

inlinevirtual

Set the input vector to the lower bound.

This function sets the input vector \(l\) to the lower bound \(a\).

Parameters

[out]

l

is the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1474 of file example_04.hpp.

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

cast_vector() [2/4]

template<class Real >

void H1BoundConstraint< Real >::cast_vector ( Teuchos::RCP< std::vector< Real > > &  xvec, ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1384 of file example_06.hpp.

cast_const_vector() [2/4]

template<class Real >

void H1BoundConstraint< Real >::cast_const_vector ( Teuchos::RCP< const std::vector< Real > > &  xvec, const ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1396 of file example_06.hpp.

axpy() [2/4]

template<class Real >

void H1BoundConstraint< Real >::axpy ( std::vector< Real > &  out, const Real  a, const std::vector< Real > &  x, const std::vector< Real > &  y  ) const

inlineprivate

Definition at line 1408 of file example_06.hpp.

projection() [2/4]

template<class Real >

void H1BoundConstraint< Real >::projection ( std::vector< Real > &  x )

inlineprivate

Definition at line 1416 of file example_06.hpp.

isFeasible() [2/4]

template<class Real >

bool H1BoundConstraint< Real >::isFeasible ( const ROL::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 1438 of file example_06.hpp.

project() [2/4]

template<class Real >

void H1BoundConstraint< Real >::project ( ROL::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 1450 of file example_06.hpp.

pruneLowerActive() [3/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1455 of file example_06.hpp.

pruneUpperActive() [3/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1466 of file example_06.hpp.

pruneActive() [3/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1477 of file example_06.hpp.

pruneLowerActive() [4/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-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 from ROL::BoundConstraint< Real >.

Definition at line 1489 of file example_06.hpp.

pruneUpperActive() [4/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 1501 of file example_06.hpp.

pruneActive() [4/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 \(\epsilon\)-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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1513 of file example_06.hpp.

setVectorToUpperBound() [2/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToUpperBound ( ROL::Vector< Real > &  u )

inlinevirtual

Set the input vector to the upper bound.

This function sets the input vector \(u\) to the upper bound \(b\).

Parameters

[out]

u

is the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1526 of file example_06.hpp.

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

setVectorToLowerBound() [2/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToLowerBound ( ROL::Vector< Real > &  l )

inlinevirtual

Set the input vector to the lower bound.

This function sets the input vector \(l\) to the lower bound \(a\).

Parameters

[out]

l

is the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1533 of file example_06.hpp.

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

cast_vector() [3/4]

template<class Real >

void H1BoundConstraint< Real >::cast_vector ( Teuchos::RCP< std::vector< Real > > &  xvec, ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1402 of file example_07.hpp.

cast_const_vector() [3/4]

template<class Real >

void H1BoundConstraint< Real >::cast_const_vector ( Teuchos::RCP< const std::vector< Real > > &  xvec, const ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1414 of file example_07.hpp.

axpy() [3/4]

template<class Real >

void H1BoundConstraint< Real >::axpy ( std::vector< Real > &  out, const Real  a, const std::vector< Real > &  x, const std::vector< Real > &  y  ) const

inlineprivate

Definition at line 1426 of file example_07.hpp.

projection() [3/4]

template<class Real >

void H1BoundConstraint< Real >::projection ( std::vector< Real > &  x )

inlineprivate

Definition at line 1434 of file example_07.hpp.

isFeasible() [3/4]

template<class Real >

bool H1BoundConstraint< Real >::isFeasible ( const ROL::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 1456 of file example_07.hpp.

project() [3/4]

template<class Real >

void H1BoundConstraint< Real >::project ( ROL::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 1468 of file example_07.hpp.

pruneLowerActive() [5/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1473 of file example_07.hpp.

pruneUpperActive() [5/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1484 of file example_07.hpp.

pruneActive() [5/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1495 of file example_07.hpp.

pruneLowerActive() [6/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-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 from ROL::BoundConstraint< Real >.

Definition at line 1507 of file example_07.hpp.

pruneUpperActive() [6/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 1519 of file example_07.hpp.

pruneActive() [6/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 \(\epsilon\)-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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1531 of file example_07.hpp.

setVectorToUpperBound() [3/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToUpperBound ( ROL::Vector< Real > &  u )

inlinevirtual

Set the input vector to the upper bound.

This function sets the input vector \(u\) to the upper bound \(b\).

Parameters

[out]

u

is the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1544 of file example_07.hpp.

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

setVectorToLowerBound() [3/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToLowerBound ( ROL::Vector< Real > &  l )

inlinevirtual

Set the input vector to the lower bound.

This function sets the input vector \(l\) to the lower bound \(a\).

Parameters

[out]

l

is the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1551 of file example_07.hpp.

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

cast_vector() [4/4]

template<class Real >

void H1BoundConstraint< Real >::cast_vector ( Teuchos::RCP< std::vector< Real > > &  xvec, ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1384 of file example_08.hpp.

cast_const_vector() [4/4]

template<class Real >

void H1BoundConstraint< Real >::cast_const_vector ( Teuchos::RCP< const std::vector< Real > > &  xvec, const ROL::Vector< Real > &  x  ) const

inlineprivate

Definition at line 1396 of file example_08.hpp.

axpy() [4/4]

template<class Real >

void H1BoundConstraint< Real >::axpy ( std::vector< Real > &  out, const Real  a, const std::vector< Real > &  x, const std::vector< Real > &  y  ) const

inlineprivate

Definition at line 1408 of file example_08.hpp.

projection() [4/4]

template<class Real >

void H1BoundConstraint< Real >::projection ( std::vector< Real > &  x )

inlineprivate

Definition at line 1416 of file example_08.hpp.

isFeasible() [4/4]

template<class Real >

bool H1BoundConstraint< Real >::isFeasible ( const ROL::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 1438 of file example_08.hpp.

project() [4/4]

template<class Real >

void H1BoundConstraint< Real >::project ( ROL::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 1450 of file example_08.hpp.

pruneLowerActive() [7/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1455 of file example_08.hpp.

pruneUpperActive() [7/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

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 1466 of file example_08.hpp.

pruneActive() [7/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1477 of file example_08.hpp.

pruneLowerActive() [8/8]

template<class Real >

void H1BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

inlinevirtual

Set variables to zero if they correspond to the lower \(\epsilon\)-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 from ROL::BoundConstraint< Real >.

Definition at line 1489 of file example_08.hpp.

pruneUpperActive() [8/8]

template<class Real >

void H1BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 1501 of file example_08.hpp.

pruneActive() [8/8]

template<class Real >

void H1BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v, const ROL::Vector< Real > &  g, const ROL::Vector< Real > &  x, Real  eps  )

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 \(\epsilon\)-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 \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1513 of file example_08.hpp.

setVectorToUpperBound() [4/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToUpperBound ( ROL::Vector< Real > &  u )

inlinevirtual

Set the input vector to the upper bound.

This function sets the input vector \(u\) to the upper bound \(b\).

Parameters

[out]

u

is the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1526 of file example_08.hpp.

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

setVectorToLowerBound() [4/4]

template<class Real >

void H1BoundConstraint< Real >::setVectorToLowerBound ( ROL::Vector< Real > &  l )

inlinevirtual

Set the input vector to the lower bound.

This function sets the input vector \(l\) to the lower bound \(a\).

Parameters

[out]

l

is the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1533 of file example_08.hpp.

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

Member Data Documentation

dim_

template<class Real >

int H1BoundConstraint< Real >::dim_

private

Definition at line 1318 of file example_04.hpp.

x_lo_

template<class Real >

std::vector< Real > H1BoundConstraint< Real >::x_lo_

private

Definition at line 1319 of file example_04.hpp.

x_up_

template<class Real >

std::vector< Real > H1BoundConstraint< Real >::x_up_

private

Definition at line 1320 of file example_04.hpp.

min_diff_

template<class Real >

Real H1BoundConstraint< Real >::min_diff_

private

Definition at line 1321 of file example_04.hpp.

scale_

template<class Real >

Real H1BoundConstraint< Real >::scale_

private

Definition at line 1322 of file example_04.hpp.

fem_

template<class Real >

Teuchos::RCP< BurgersFEM< Real > > H1BoundConstraint< Real >::fem_

private

Definition at line 1323 of file example_04.hpp.

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The documentation for this class was generated from the following files:

• example_04.hpp
• example_06.hpp
• example_07.hpp
• example_08.hpp