ROL
Public Member Functions | Private Member Functions | Private Attributes | List of all members
L2BoundConstraint< Real > Class Template Reference

#include <example_04.hpp>

+ Inheritance diagram for L2BoundConstraint< Real >:

Public Member Functions

 L2BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const ROL::Ptr< 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=Real(0))
 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=Real(0))
 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=Real(0))
 
void pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
 
void pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
 
void pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getLowerBound (void) const
 Return the ref count pointer to the lower bound vector. More...
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getUpperBound (void) const
 Return the ref count pointer to the upper bound vector. More...
 
 L2BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const ROL::Ptr< 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=Real(0))
 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=Real(0))
 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=Real(0))
 
void pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
 
void pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
 
void pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getLowerBound (void) const
 Return the ref count pointer to the lower bound vector. More...
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getUpperBound (void) const
 Return the ref count pointer to the upper bound vector. More...
 
 L2BoundConstraint (std::vector< Real > &l, std::vector< Real > &u, const ROL::Ptr< 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=Real(0))
 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=Real(0))
 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=Real(0))
 
void pruneLowerActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
 
void pruneUpperActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the upper \(\epsilon\)-binding set. More...
 
void pruneActive (ROL::Vector< Real > &v, const ROL::Vector< Real > &g, const ROL::Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getLowerBound (void) const
 Return the ref count pointer to the lower bound vector. More...
 
const ROL::Ptr< const
ROL::Vector< Real > > 		getUpperBound (void) const
 Return the ref count pointer to the upper bound vector. More...
 
- Public Member Functions inherited from ROL::BoundConstraint< Real >
virtual ~BoundConstraint ()
 
 BoundConstraint (void)
 
 BoundConstraint (const Vector< Real > &x)
 
virtual void projectInterior (Vector< Real > &x)
 Project optimization variables into the interior of the feasible set. More...
 
virtual void applyInverseScalingFunction (Vector< Real > &dv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g) const
 Apply inverse scaling function. More...
 
virtual void applyScalingFunctionJacobian (Vector< Real > &dv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g) const
 Apply scaling function Jacobian. More...
 
void activateLower (void)
 Turn on lower bound. More...
 
void activateUpper (void)
 Turn on upper bound. More...
 
void activate (void)
 Turn on bounds. More...
 
void deactivateLower (void)
 Turn off lower bound. More...
 
void deactivateUpper (void)
 Turn off upper bound. More...
 
void deactivate (void)
 Turn off bounds. More...
 
bool isLowerActivated (void) const
 Check if lower bound are on. More...
 
bool isUpperActivated (void) const
 Check if upper bound are on. More...
 
bool isActivated (void) const
 Check if bounds are on. More...
 
void pruneActive (Vector< Real > &v, const Vector< Real > &x, Real eps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-active set. More...
 
void pruneActive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-binding set. More...
 
void pruneLowerInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...
 
void pruneUpperInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...
 
void pruneLowerInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...
 
void pruneUpperInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...
 
void pruneInactive (Vector< Real > &v, const Vector< Real > &x, Real eps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-inactive set. More...
 
void pruneInactive (Vector< Real > &v, const Vector< Real > &g, const Vector< Real > &x, Real xeps=Real(0), Real geps=Real(0))
 Set variables to zero if they correspond to the \(\epsilon\)-nonbinding set. More...
 
void computeProjectedGradient (Vector< Real > &g, const Vector< Real > &x)
 Compute projected gradient. More...
 
void computeProjectedStep (Vector< Real > &v, const Vector< Real > &x)
 Compute projected step. More...
 

Private Member Functions

void cast_vector (ROL::Ptr< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
 
void cast_const_vector (ROL::Ptr< 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 (ROL::Ptr< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
 
void cast_const_vector (ROL::Ptr< 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 (ROL::Ptr< std::vector< Real > > &xvec, ROL::Vector< Real > &x) const
 
void cast_const_vector (ROL::Ptr< 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_
 
ROL::Ptr< BurgersFEM< Real > > fem_
 
ROL::Ptr< ROL::Vector< Real > > l_
 
ROL::Ptr< ROL::Vector< Real > > u_
 

Additional Inherited Members

- Protected Member Functions inherited from ROL::BoundConstraint< Real >
Real computeInf (const Vector< Real > &x) const
 
- Protected Attributes inherited from ROL::BoundConstraint< Real >
Ptr< Vector< Real > > lower_
 
Ptr< Vector< Real > > upper_
 

Detailed Description

template<class Real>
class L2BoundConstraint< Real >

Definition at line 1139 of file example_04.hpp.

Constructor & Destructor Documentation

template<class Real >
L2BoundConstraint< Real >::L2BoundConstraint ( std::vector< Real > &  l,
std::vector< Real > &  u,
const ROL::Ptr< BurgersFEM< Real > > &  fem,
Real  scale = 1.0 
)
inline

Definition at line 1185 of file example_04.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::l_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::u_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
L2BoundConstraint< Real >::L2BoundConstraint ( std::vector< Real > &  l,
std::vector< Real > &  u,
const ROL::Ptr< BurgersFEM< Real > > &  fem,
Real  scale = 1.0 
)
inline

Definition at line 1262 of file example_07.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::l_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::u_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
L2BoundConstraint< Real >::L2BoundConstraint ( std::vector< Real > &  l,
std::vector< Real > &  u,
const ROL::Ptr< BurgersFEM< Real > > &  fem,
Real  scale = 1.0 
)
inline

Definition at line 1048 of file example_08.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::l_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::u_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

Member Function Documentation

template<class Real >
void L2BoundConstraint< Real >::cast_vector ( ROL::Ptr< std::vector< Real > > &  xvec,
ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1150 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::project(), L2BoundConstraint< Real >::pruneActive(), L2BoundConstraint< Real >::pruneLowerActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
void L2BoundConstraint< Real >::cast_const_vector ( ROL::Ptr< const std::vector< Real > > &  xvec,
const ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1160 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::isFeasible(), L2BoundConstraint< Real >::pruneActive(), L2BoundConstraint< Real >::pruneLowerActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
void L2BoundConstraint< Real >::axpy ( std::vector< Real > &  out,
const Real  a,
const std::vector< Real > &  x,
const std::vector< Real > &  y 
) const
inlineprivate

Definition at line 1170 of file example_04.hpp.

References L2BoundConstraint< Real >::dim_.

template<class Real >
void L2BoundConstraint< Real >::projection ( std::vector< Real > &  x)
inlineprivate

Definition at line 1178 of file example_04.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

Referenced by L2BoundConstraint< Real >::project().

template<class Real >
bool L2BoundConstraint< 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 1204 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< 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 1216 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_vector(), and L2BoundConstraint< Real >::projection().

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1221 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1232 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inline

Definition at line 1243 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1255 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1267 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inline

Definition at line 1279 of file example_04.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getLowerBound ( void  ) const
inlinevirtual

Return the ref count pointer to the lower bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1292 of file example_04.hpp.

References L2BoundConstraint< Real >::l_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getUpperBound ( void  ) const
inlinevirtual

Return the ref count pointer to the upper bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1296 of file example_04.hpp.

References L2BoundConstraint< Real >::u_.

template<class Real >
void L2BoundConstraint< Real >::cast_vector ( ROL::Ptr< std::vector< Real > > &  xvec,
ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1227 of file example_07.hpp.

template<class Real >
void L2BoundConstraint< Real >::cast_const_vector ( ROL::Ptr< const std::vector< Real > > &  xvec,
const ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1237 of file example_07.hpp.

template<class Real >
void L2BoundConstraint< Real >::axpy ( std::vector< Real > &  out,
const Real  a,
const std::vector< Real > &  x,
const std::vector< Real > &  y 
) const
inlineprivate

Definition at line 1247 of file example_07.hpp.

References L2BoundConstraint< Real >::dim_.

template<class Real >
void L2BoundConstraint< Real >::projection ( std::vector< Real > &  x)
inlineprivate

Definition at line 1255 of file example_07.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
bool L2BoundConstraint< 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 1281 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< 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 1293 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_vector(), and L2BoundConstraint< Real >::projection().

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1298 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1309 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inline

Definition at line 1320 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1332 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1344 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inline

Definition at line 1356 of file example_07.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getLowerBound ( void  ) const
inlinevirtual

Return the ref count pointer to the lower bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1369 of file example_07.hpp.

References L2BoundConstraint< Real >::l_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getUpperBound ( void  ) const
inlinevirtual

Return the ref count pointer to the upper bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1373 of file example_07.hpp.

References L2BoundConstraint< Real >::u_.

template<class Real >
void L2BoundConstraint< Real >::cast_vector ( ROL::Ptr< std::vector< Real > > &  xvec,
ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1013 of file example_08.hpp.

template<class Real >
void L2BoundConstraint< Real >::cast_const_vector ( ROL::Ptr< const std::vector< Real > > &  xvec,
const ROL::Vector< Real > &  x 
) const
inlineprivate

Definition at line 1023 of file example_08.hpp.

template<class Real >
void L2BoundConstraint< Real >::axpy ( std::vector< Real > &  out,
const Real  a,
const std::vector< Real > &  x,
const std::vector< Real > &  y 
) const
inlineprivate

Definition at line 1033 of file example_08.hpp.

References L2BoundConstraint< Real >::dim_.

template<class Real >
void L2BoundConstraint< Real >::projection ( std::vector< Real > &  x)
inlineprivate

Definition at line 1041 of file example_08.hpp.

References L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
bool L2BoundConstraint< 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 1067 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< 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 1079 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_vector(), and L2BoundConstraint< Real >::projection().

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1084 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{A}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-active set is defined as

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

Parameters
[out]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 1095 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  x,
Real  eps = Real(0) 
)
inline

Definition at line 1106 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneLowerActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^-_\epsilon(x)\). Here, the lower \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1118 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_lo_.

template<class Real >
void L2BoundConstraint< Real >::pruneUpperActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inlinevirtual

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

This function sets \(v(\xi)=0\) if \(\xi\in\mathcal{B}^+_\epsilon(x)\). Here, the upper \(\epsilon\)-binding set is defined as

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

Parameters
[out]vis the variable to be pruned.
[in]gis the negative search direction.
[in]xis the current optimization variable.
[in]xepsis the active-set tolerance \(\epsilon_x\).
[in]gepsis the binding-set tolerance \(\epsilon_g\).

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1130 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
void L2BoundConstraint< Real >::pruneActive ( ROL::Vector< Real > &  v,
const ROL::Vector< Real > &  g,
const ROL::Vector< Real > &  x,
Real  xeps = Real(0),
Real  geps = Real(0) 
)
inline

Definition at line 1142 of file example_08.hpp.

References L2BoundConstraint< Real >::cast_const_vector(), L2BoundConstraint< Real >::cast_vector(), L2BoundConstraint< Real >::dim_, L2BoundConstraint< Real >::min_diff_, L2BoundConstraint< Real >::scale_, L2BoundConstraint< Real >::x_lo_, and L2BoundConstraint< Real >::x_up_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getLowerBound ( void  ) const
inlinevirtual

Return the ref count pointer to the lower bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1155 of file example_08.hpp.

References L2BoundConstraint< Real >::l_.

template<class Real >
const ROL::Ptr<const ROL::Vector<Real> > L2BoundConstraint< Real >::getUpperBound ( void  ) const
inlinevirtual

Return the ref count pointer to the upper bound vector.

Reimplemented from ROL::BoundConstraint< Real >.

Definition at line 1159 of file example_08.hpp.

References L2BoundConstraint< Real >::u_.

Member Data Documentation

template<class Real >
int L2BoundConstraint< Real >::dim_
private

Definition at line 1141 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::axpy(), L2BoundConstraint< Real >::isFeasible(), L2BoundConstraint< Real >::L2BoundConstraint(), L2BoundConstraint< Real >::projection(), L2BoundConstraint< Real >::pruneActive(), L2BoundConstraint< Real >::pruneLowerActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
std::vector< Real > L2BoundConstraint< Real >::x_lo_
private

Definition at line 1142 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::isFeasible(), L2BoundConstraint< Real >::L2BoundConstraint(), L2BoundConstraint< Real >::projection(), L2BoundConstraint< Real >::pruneActive(), and L2BoundConstraint< Real >::pruneLowerActive().

template<class Real >
std::vector< Real > L2BoundConstraint< Real >::x_up_
private

Definition at line 1143 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::isFeasible(), L2BoundConstraint< Real >::L2BoundConstraint(), L2BoundConstraint< Real >::projection(), L2BoundConstraint< Real >::pruneActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
Real L2BoundConstraint< Real >::min_diff_
private

Definition at line 1144 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::L2BoundConstraint(), L2BoundConstraint< Real >::pruneActive(), L2BoundConstraint< Real >::pruneLowerActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
Real L2BoundConstraint< Real >::scale_
private

Definition at line 1145 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::pruneActive(), L2BoundConstraint< Real >::pruneLowerActive(), and L2BoundConstraint< Real >::pruneUpperActive().

template<class Real >
ROL::Ptr< BurgersFEM< Real > > L2BoundConstraint< Real >::fem_
private

Definition at line 1146 of file example_04.hpp.

template<class Real >
ROL::Ptr< ROL::Vector< Real > > L2BoundConstraint< Real >::l_
private

Definition at line 1147 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::getLowerBound(), and L2BoundConstraint< Real >::L2BoundConstraint().

template<class Real >
ROL::Ptr< ROL::Vector< Real > > L2BoundConstraint< Real >::u_
private

Definition at line 1148 of file example_04.hpp.

Referenced by L2BoundConstraint< Real >::getUpperBound(), and L2BoundConstraint< Real >::L2BoundConstraint().

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