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ROL::BoundConstraint< Real > Class Template Reference

Provides the interface to apply upper and lower bound constraints. More...

#include <ROL_BoundConstraint.hpp>

+ Inheritance diagram for ROL::BoundConstraint< Real >:

Classes

class  Active
 
class  LowerBinding
 
class  PruneBinding
 
class  UpperBinding
 

Public Member Functions

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...
 
virtual void project (Vector< Real > &x)
 Project optimization variables onto the bounds. More...
 
virtual void pruneUpperActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the upper \(\epsilon\)-active set. More...
 
virtual void pruneUpperActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
 
virtual void pruneLowerActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the lower \(\epsilon\)-active set. More...
 
virtual void pruneLowerActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the lower \(\epsilon\)-binding set. 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...
 
virtual void setVectorToUpperBound (Vector< Real > &u)
 Set the input vector to the upper bound. More...
 
virtual void setVectorToLowerBound (Vector< Real > &l)
 Set the input vector to the lower bound. More...
 
virtual void pruneActive (Vector< Real > &v, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
 
virtual void pruneActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real eps=0.0)
 Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
 
virtual bool isFeasible (const Vector< Real > &v)
 Check if the vector, v, is feasible. 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 Attributes

int dim_
 
const Teuchos::RCP< Vector< Real > > x_lo_
 
const Teuchos::RCP< Vector< Real > > x_up_
 
const Real scale_
 
Teuchos::RCP< Vector< Real > > mask_
 
bool activated_
 Flag that determines whether or not the constraints are being used. More...
 
Real min_diff_
 
Elementwise::ReductionMin< Real > minimum_
 
ROL::BoundConstraint::PruneBinding prune_
 

Detailed Description

template<class Real>
class ROL::BoundConstraint< Real >

Provides the interface to apply upper and lower bound constraints.

ROL's bound constraint class is to designed to handle point wise bound constraints on optimization variables. That is, let \(\mathcal{X}\) be a Banach space of functions from \(\Xi\) into \(\mathbb{R}\) (for example, \(\Xi\subset\mathbb{R}^d\) for some positive integer \(d\) and \(\mathcal{X}=L^2(\Xi)\) or \(\Xi = \{1,\ldots,n\}\) and \(\mathcal{X}=\mathbb{R}^n\)). For any \(x\in\mathcal{X}\), we consider bounds of the form

\[ a(\xi) \le x(\xi) \le b(\xi) \quad \text{for almost every }\xi\in\Xi. \]

Here, \(a(\xi)\le b(\xi)\) for almost every \(\xi\in\Xi\) and \(a,b\in \mathcal{X}\).

Definition at line 72 of file ROL_BoundConstraint.hpp.

Constructor & Destructor Documentation

template<class Real>
virtual ROL::BoundConstraint< Real >::~BoundConstraint ( )
inlinevirtual

Definition at line 126 of file ROL_BoundConstraint.hpp.

template<class Real>
ROL::BoundConstraint< Real >::BoundConstraint ( void  )
inline

Definition at line 128 of file ROL_BoundConstraint.hpp.

template<class Real>
ROL::BoundConstraint< Real >::BoundConstraint ( const Teuchos::RCP< Vector< Real > > &  x_lo,
const Teuchos::RCP< Vector< Real > > &  x_up,
const Real  scale = 1.0 
)
inline

Default constructor.

The default constructor automatically turns the constraints on.

Definition at line 136 of file ROL_BoundConstraint.hpp.

Member Function Documentation

template<class Real>
virtual void ROL::BoundConstraint< Real >::update ( const Vector< Real > &  x,
bool  flag = true,
int  iter = -1 
)
inlinevirtual

Update bounds.

The update function allows the user to update the bounds at each new iterations.

Parameters
[in]xis the optimization variable.
[in]flagis set to true if control is changed.
[in]iteris the outer algorithm iterations count.

Reimplemented in ROL::BoundConstraint_SimOpt< Real >, and ROL::RiskBoundConstraint< Real >.

Definition at line 159 of file ROL_BoundConstraint.hpp.

Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().

template<class Real>
virtual void ROL::BoundConstraint< 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]xis the optimization variable.

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 169 of file ROL_BoundConstraint.hpp.

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

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::TrustRegionStep< Real >::compute(), ROL::LineSearchStep< Real >::compute(), ROL::PrimalDualActiveSetStep< Real >::computeCriticalityMeasure(), ROL::TrustRegionStep< Real >::computeCriticalityMeasure(), ROL::AugmentedLagrangianStep< Real >::computeGradient(), ROL::BoundConstraint< Real >::computeProjectedStep(), ROL::Step< Real >::initialize(), ROL::AugmentedLagrangianStep< Real >::initialize(), ROL::MoreauYosidaPenaltyStep< Real >::initialize(), ROL::PrimalDualActiveSetStep< Real >::initialize(), ROL::TrustRegionStep< Real >::initialize(), ROL::TrustRegionStep< Real >::update(), ROL::LineSearchStep< Real >::update(), ROL::LineSearch< Real >::updateIterate(), and ROL::MoreauYosidaPenaltyStep< Real >::updateState().

template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneUpperActive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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

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

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

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 195 of file ROL_BoundConstraint.hpp.

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

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint< Real >::pruneActive(), and ROL::BoundConstraint< Real >::pruneUpperInactive().

template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneUpperActive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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

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

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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::StdBoundConstraint< Real >, and ROL::RiskBoundConstraint< Real >.

Definition at line 220 of file ROL_BoundConstraint.hpp.

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

template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneLowerActive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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

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

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

Reimplemented in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 245 of file ROL_BoundConstraint.hpp.

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

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::BoundConstraint< Real >::pruneActive(), and ROL::BoundConstraint< Real >::pruneLowerInactive().

template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneLowerActive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, BoundConstraint_BurgersControl< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 270 of file ROL_BoundConstraint.hpp.

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

template<class Real>
const Teuchos::RCP<Vector<Real> > ROL::BoundConstraint< Real >::getLowerVectorRCP ( void  ) const
inline

Return the ref count pointer to the lower bound vector.

Definition at line 285 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::x_lo_.

template<class Real>
const Teuchos::RCP<Vector<Real> > ROL::BoundConstraint< Real >::getUpperVectorRCP ( void  ) const
inline

Return the ref count pointer to the upper bound vector.

Definition at line 290 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::x_up_.

template<class Real>
virtual void ROL::BoundConstraint< Real >::setVectorToUpperBound ( Vector< Real > &  u)
inlinevirtual
template<class Real>
virtual void ROL::BoundConstraint< Real >::setVectorToLowerBound ( Vector< Real > &  l)
inlinevirtual
template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneActive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 326 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::pruneLowerActive(), and ROL::BoundConstraint< Real >::pruneUpperActive().

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::LineSearchStep< Real >::compute(), ROL::BoundConstraint< Real >::computeProjectedGradient(), ROL::BoundConstraint< Real >::pruneInactive(), and ROL::LineSearch< Real >::status().

template<class Real>
virtual void ROL::BoundConstraint< Real >::pruneActive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
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 \(\epsilon\)-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 in H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, H1BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, L2BoundConstraint< Real >, ROL::BoundConstraint_SimOpt< Real >, ROL::RiskBoundConstraint< Real >, and ROL::StdBoundConstraint< Real >.

Definition at line 343 of file ROL_BoundConstraint.hpp.

References ROL::BoundConstraint< Real >::pruneLowerActive(), and ROL::BoundConstraint< Real >::pruneUpperActive().

template<class Real>
virtual bool ROL::BoundConstraint< Real >::isFeasible ( const Vector< Real > &  v)
inlinevirtual
template<class Real>
void ROL::BoundConstraint< Real >::activate ( void  )
inline

Turn on bounds.

This function turns the bounds on.

Definition at line 373 of file ROL_BoundConstraint.hpp.

Referenced by ROL::BoundConstraint_SimOpt< Real >::BoundConstraint_SimOpt().

template<class Real>
void ROL::BoundConstraint< Real >::deactivate ( void  )
inline
template<class Real>
bool ROL::BoundConstraint< Real >::isActivated ( void  )
inline
template<class Real>
void ROL::BoundConstraint< Real >::pruneInactive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline

Set variables to zero if they correspond to the \(\epsilon\)-inactive set.

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{A}_\epsilon(x)\). Here,

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

Definition at line 394 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), and ROL::BoundConstraint< Real >::pruneActive().

Referenced by ROL::LineSearchStep< Real >::compute(), and ROL::LineSearch< Real >::status().

template<class Real>
void ROL::BoundConstraint< Real >::pruneLowerInactive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline
template<class Real>
void ROL::BoundConstraint< Real >::pruneUpperInactive ( Vector< Real > &  v,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline
template<class Real>
void ROL::BoundConstraint< Real >::pruneInactive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline

Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set.

This function sets \(v(\xi)=0\) if \(\xi\in\Xi\setminus\mathcal{B}_\epsilon(x)\).

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 \(\epsilon\).

Definition at line 422 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), and ROL::BoundConstraint< Real >::pruneActive().

template<class Real>
void ROL::BoundConstraint< Real >::pruneLowerInactive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline
template<class Real>
void ROL::BoundConstraint< Real >::pruneUpperInactive ( Vector< Real > &  v,
const Vector< Real > &  g,
const Vector< Real > &  x,
Real  eps = 0.0 
)
inline
template<class Real>
void ROL::BoundConstraint< Real >::computeProjectedGradient ( Vector< Real > &  g,
const Vector< Real > &  x 
)
inline

Compute projected gradient.

This function projects the gradient \(g\) onto the tangent cone.

Parameters
[in,out]gis the gradient of the objective function at x.
[in]xis the optimization variable

Definition at line 447 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::clone(), and ROL::BoundConstraint< Real >::pruneActive().

Referenced by ROL::TrustRegionStep< Real >::computeCriticalityMeasure(), and ROL::LineSearchStep< Real >::update().

template<class Real>
void ROL::BoundConstraint< Real >::computeProjectedStep ( Vector< Real > &  v,
const Vector< Real > &  x 
)
inline

Compute projected step.

This function computes the projected step \(P_{[a,b]}(x+v) - x\).

Parameters
[in,out]vis the step variable.
[in]xis the optimization variable.

Definition at line 459 of file ROL_BoundConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::plus(), and ROL::BoundConstraint< Real >::project().

Member Data Documentation

template<class Real>
int ROL::BoundConstraint< Real >::dim_
private

Definition at line 74 of file ROL_BoundConstraint.hpp.

template<class Real>
const Teuchos::RCP<Vector<Real> > ROL::BoundConstraint< Real >::x_lo_
private
template<class Real>
const Teuchos::RCP<Vector<Real> > ROL::BoundConstraint< Real >::x_up_
private
template<class Real>
const Real ROL::BoundConstraint< Real >::scale_
private

Definition at line 78 of file ROL_BoundConstraint.hpp.

template<class Real>
Teuchos::RCP<Vector<Real> > ROL::BoundConstraint< Real >::mask_
private

Definition at line 80 of file ROL_BoundConstraint.hpp.

template<class Real>
bool ROL::BoundConstraint< Real >::activated_
private

Flag that determines whether or not the constraints are being used.

Definition at line 82 of file ROL_BoundConstraint.hpp.

Referenced by ROL::BoundConstraint< Real >::isActivated().

template<class Real>
Real ROL::BoundConstraint< Real >::min_diff_
private

Definition at line 83 of file ROL_BoundConstraint.hpp.

template<class Real>
Elementwise::ReductionMin<Real> ROL::BoundConstraint< Real >::minimum_
private

Definition at line 85 of file ROL_BoundConstraint.hpp.

template<class Real>
ROL::BoundConstraint::PruneBinding ROL::BoundConstraint< Real >::prune_
private

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