ROL
Public Member Functions | Private Attributes | List of all members
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 >:

Public Member Functions

virtual ~BoundConstraint ()
 
 BoundConstraint (void)
 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...
 
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 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 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

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

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 78 of file ROL_BoundConstraint.hpp.

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

Default constructor.

The default constructor automatically turns the constraints on.

Definition at line 84 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::CVaRBoundConstraint< Real >.

Definition at line 93 of file ROL_BoundConstraint.hpp.

template<class Real>
virtual void ROL::BoundConstraint< Real >::project ( Vector< Real > &  x)
inlinevirtual
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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, BoundConstraint_PoissonControl< Real >, ROL::StdBoundConstraint< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 116 of file ROL_BoundConstraint.hpp.

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

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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, ROL::StdBoundConstraint< Real >, BoundConstraint_PoissonControl< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 131 of file ROL_BoundConstraint.hpp.

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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, BoundConstraint_PoissonControl< Real >, ROL::StdBoundConstraint< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 144 of file ROL_BoundConstraint.hpp.

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

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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, ROL::StdBoundConstraint< Real >, BoundConstraint_PoissonControl< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 159 of file ROL_BoundConstraint.hpp.

template<class Real>
virtual void ROL::BoundConstraint< Real >::setVectorToUpperBound ( 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 in ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, ROL::StdBoundConstraint< Real >, BoundConstraint_PoissonControl< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 166 of file ROL_BoundConstraint.hpp.

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute().

template<class Real>
virtual void ROL::BoundConstraint< Real >::setVectorToLowerBound ( 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 in ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, BoundConstraint_BurgersControl< Real >, BoundConstraint_PoissonInversion< Real >, ROL::StdBoundConstraint< Real >, BoundConstraint_PoissonControl< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 173 of file ROL_BoundConstraint.hpp.

Referenced by ROL::PrimalDualActiveSetStep< Real >::compute().

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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, ROL::StdBoundConstraint< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 186 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 ROL::ZOO::BoundConstraint_DiodeCircuit< Real >, ROL::StdBoundConstraint< Real >, and ROL::CVaRBoundConstraint< Real >.

Definition at line 203 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 236 of file ROL_BoundConstraint.hpp.

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

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

Turn off bounds.

This function turns the bounds off.

Definition at line 242 of file ROL_BoundConstraint.hpp.

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

Referenced by ROL::DefaultAlgorithm< Real >::run().

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 257 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 >::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 272 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 >::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 285 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 297 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>
bool ROL::BoundConstraint< Real >::activated_
private

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