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 1173 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 1219 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 1296 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 1082 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 1184 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 1194 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 1204 of file example_04.hpp.

References L2BoundConstraint< Real >::dim_.

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

Definition at line 1212 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 1238 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 1250 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 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 > &  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 1266 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 1277 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 1289 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 1301 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 1313 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 1326 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 1330 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 1261 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 1271 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 1281 of file example_07.hpp.

References L2BoundConstraint< Real >::dim_.

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

Definition at line 1289 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 1315 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 1327 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 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 > &  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 1343 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 1354 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 1366 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 1378 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 1390 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 1403 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 1407 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 1047 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 1057 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 1067 of file example_08.hpp.

References L2BoundConstraint< Real >::dim_.

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

Definition at line 1075 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 1101 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 1113 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 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 > &  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 1129 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 1140 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 1152 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 1164 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 1176 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 1189 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 1193 of file example_08.hpp.

References L2BoundConstraint< Real >::u_.

Member Data Documentation

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

Definition at line 1175 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 1176 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 1177 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 1178 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 1179 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 1180 of file example_04.hpp.

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

Definition at line 1181 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 1182 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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