ROL
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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 Teuchos::RCP< Vector< Real > > &x_lo, const Teuchos::RCP< Vector< Real > > &x_up, const Real scale=1.0)
 Default constructor. More...
 
virtual void update (const Vector< Real > &x, bool flag=true, int iter=-1)
 Update bounds. More...
 
const Teuchos::RCP< Vector< Real > > getLowerVectorRCP (void) const
 Return the ref count pointer to the lower bound vector. More...
 
const Teuchos::RCP< Vector< Real > > getUpperVectorRCP (void) const
 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=0.0)
 Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...
 
void pruneLowerInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
 
void pruneUpperInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
 
void pruneInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
 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=0.0)
 
void pruneUpperInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
 
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

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.

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 1421 of file example_06.hpp.

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 1437 of file example_07.hpp.

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 1421 of file example_08.hpp.

Member Function Documentation

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.

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.

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.

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

Definition at line 1357 of file example_04.hpp.

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]vis the vector to be checked.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1379 of file example_04.hpp.

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]xis the optimization variable.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1391 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1396 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1407 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1418 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1430 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1442 of file example_04.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1454 of file example_04.hpp.

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]uis 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().

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]lis 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().

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

Definition at line 1382 of file example_06.hpp.

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 1394 of file example_06.hpp.

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 1406 of file example_06.hpp.

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

Definition at line 1414 of file example_06.hpp.

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]vis the vector to be checked.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1436 of file example_06.hpp.

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]xis the optimization variable.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1448 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1453 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1464 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1475 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1487 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1499 of file example_06.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1511 of file example_06.hpp.

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]uis the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1524 of file example_06.hpp.

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

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]lis the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1531 of file example_06.hpp.

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

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

Definition at line 1398 of file example_07.hpp.

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 1410 of file example_07.hpp.

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 1422 of file example_07.hpp.

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

Definition at line 1430 of file example_07.hpp.

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]vis the vector to be checked.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1452 of file example_07.hpp.

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]xis the optimization variable.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1464 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1469 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1480 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1491 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1503 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1515 of file example_07.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1527 of file example_07.hpp.

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]uis the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1540 of file example_07.hpp.

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

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]lis the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1547 of file example_07.hpp.

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

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

Definition at line 1382 of file example_08.hpp.

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 1394 of file example_08.hpp.

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 1406 of file example_08.hpp.

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

Definition at line 1414 of file example_08.hpp.

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]vis the vector to be checked.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1436 of file example_08.hpp.

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]xis the optimization variable.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1448 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1453 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1464 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1475 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1487 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1499 of file example_08.hpp.

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]vis the variable to be pruned.
[in]xis the current optimization variable.
[in]gis the negative search direction.
[in]epsis the active-set tolerance \(\epsilon\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1511 of file example_08.hpp.

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]uis the vector to be set to the upper bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1524 of file example_08.hpp.

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

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]lis the vector to be set to the lower bound.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1531 of file example_08.hpp.

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

Member Data Documentation

template<class Real >
int H1BoundConstraint< Real >::dim_
private

Definition at line 1318 of file example_04.hpp.

template<class Real >
std::vector< Real > H1BoundConstraint< Real >::x_lo_
private

Definition at line 1319 of file example_04.hpp.

template<class Real >
std::vector< Real > H1BoundConstraint< Real >::x_up_
private

Definition at line 1320 of file example_04.hpp.

template<class Real >
Real H1BoundConstraint< Real >::min_diff_
private

Definition at line 1321 of file example_04.hpp.

template<class Real >
Real H1BoundConstraint< Real >::scale_
private

Definition at line 1322 of file example_04.hpp.

template<class Real >
Teuchos::RCP< BurgersFEM< Real > > H1BoundConstraint< Real >::fem_
private

Definition at line 1323 of file example_04.hpp.


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