Provides an implementation for lower bound constraints. More...

#include <ROL_LowerBoundToConstraint.hpp>

Inheritance diagram for ROL::LowerBoundToConstraint< Real >:

Public Member Functions
	LowerBoundToConstraint (BoundConstraint< Real > &bnd)

	LowerBoundToConstraint (const Vector< Real > &lo)

void	value (Vector< Real > &c, const Vector< Real > &x, Real &tol)
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...

void	applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\). More...

void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\). More...

void	applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \). More...

Public Member Functions inherited from ROL::Constraint< Real >
virtual	~Constraint (void)

	Constraint (void)

virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count. More...

virtual void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualv, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\). More...

virtual std::vector< Real >	solveAugmentedSystem (Vector< Real > &v1, Vector< Real > &v2, const Vector< Real > &b1, const Vector< Real > &b2, const Vector< Real > &x, Real &tol)
	Approximately solves the augmented system \[ \begin{pmatrix} I & c'(x)^* \\ c'(x) & 0 \end{pmatrix} \begin{pmatrix} v_{1} \\ v_{2} \end{pmatrix} = \begin{pmatrix} b_{1} \\ b_{2} \end{pmatrix} \] where \(v_{1} \in \mathcal{X}\), \(v_{2} \in \mathcal{C}^\), \(b_{1} \in \mathcal{X}^\), \(b_{2} \in \mathcal{C}\), \(I : \mathcal{X} \rightarrow \mathcal{X}^\) is an identity or Riesz operator, and \(0 : \mathcal{C}^ \rightarrow \mathcal{C}\) is a zero operator. More...

virtual void	applyPreconditioner (Vector< Real > &pv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g, Real &tol)
	Apply a constraint preconditioner at \(x\), \(P(x) \in L(\mathcal{C}, \mathcal{C}^)\), to vector \(v\). Ideally, this preconditioner satisfies the following relationship: \[ \left[c'(x) \circ R \circ c'(x)^ \circ P(x)\right] v = v \,, \] where R is the appropriate Riesz map in \(L(\mathcal{X}^*, \mathcal{X})\). It is used by the solveAugmentedSystem method. More...

void	activate (void)
	Turn on constraints. More...

void	deactivate (void)
	Turn off constraints. More...

bool	isActivated (void)
	Check if constraints are on. More...

virtual std::vector < std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the constraint Jacobian application. More...

virtual std::vector < std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the constraint Jacobian application. More...

virtual std::vector < std::vector< Real > >	checkApplyAdjointJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &c, const Vector< Real > &ajv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference check for the application of the adjoint of constraint Jacobian. More...

virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const bool printToStream=true, std::ostream &outStream=std::cout)

virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualw, const Vector< Real > &dualv, const bool printToStream=true, std::ostream &outStream=std::cout)

virtual std::vector < std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const std::vector< Real > &step, const bool printToScreen=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian. More...

virtual std::vector < std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const bool printToScreen=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian. More...

virtual void	setParameter (const std::vector< Real > &param)

Private Attributes
ROL::Ptr< Vector< Real > >	lo_

Additional Inherited Members
Protected Member Functions inherited from ROL::Constraint< Real >
const std::vector< Real >	getParameter (void) const

Detailed Description

template<class Real>
class ROL::LowerBoundToConstraint< Real >

Provides an implementation for lower bound constraints.

Definition at line 57 of file ROL_LowerBoundToConstraint.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::LowerBoundToConstraint< Real >::LowerBoundToConstraint ( BoundConstraint< Real > & bnd )

inline

Definition at line 62 of file ROL_LowerBoundToConstraint.hpp.

References ROL::BoundConstraint< Real >::getLowerBound(), and ROL::LowerBoundToConstraint< Real >::lo_.

template<class Real >

ROL::LowerBoundToConstraint< Real >::LowerBoundToConstraint ( const Vector< Real > & lo )

inline

Definition at line 67 of file ROL_LowerBoundToConstraint.hpp.

References ROL::Vector< Real >::clone(), and ROL::LowerBoundToConstraint< Real >::lo_.

Member Function Documentation

template<class Real >

void ROL::LowerBoundToConstraint< Real >::value	(	Vector< Real > &	c,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).

Parameters

[out]	c	is the result of evaluating the constraint operator at x; a constraint-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{c} = c(x)\), where \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

Implements ROL::Constraint< Real >.

Definition at line 72 of file ROL_LowerBoundToConstraint.hpp.

References ROL::Vector< Real >::axpy(), ROL::LowerBoundToConstraint< Real >::lo_, and ROL::Vector< Real >::set().

template<class Real >

void ROL::LowerBoundToConstraint< Real >::applyJacobian	(	Vector< Real > &	jv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).

  @param[out]      jv  is the result of applying the constraint Jacobian to @b v at @b x; a constraint-space vector
  @param[in]       v   is an optimization-space vector
  @param[in]       x   is the constraint argument; an optimization-space vector
  @param[in,out]   tol is a tolerance for inexact evaluations; currently unused

  On return, \form#76, where

\(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::Constraint< Real >.

Definition at line 77 of file ROL_LowerBoundToConstraint.hpp.

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

template<class Real >

void ROL::LowerBoundToConstraint< Real >::applyAdjointJacobian	(	Vector< Real > &	ajv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^*, \mathcal{X}^*)\), to vector \(v\).

  @param[out]      ajv is the result of applying the adjoint of the constraint Jacobian to @b v at @b x; a dual optimization-space vector
  @param[in]       v   is a dual constraint-space vector
  @param[in]       x   is the constraint argument; an optimization-space vector
  @param[in,out]   tol is a tolerance for inexact evaluations; currently unused

  On return, \form#80, where

\(v \in \mathcal{C}^*\), \(\mathsf{ajv} \in \mathcal{X}^*\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::Constraint< Real >.

Definition at line 81 of file ROL_LowerBoundToConstraint.hpp.

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

template<class Real >

void ROL::LowerBoundToConstraint< Real >::applyAdjointHessian	(	Vector< Real > &	ahuv,
		const Vector< Real > &	u,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \).

  @param[out]      ahuv is the result of applying the derivative of the adjoint of the constraint Jacobian at @b x to vector @b u in direction @b v; a dual optimization-space vector
  @param[in]       u    is the direction vector; a dual constraint-space vector
  @param[in]       v    is an optimization-space vector
  @param[in]       x    is the constraint argument; an optimization-space vector
  @param[in,out]   tol  is a tolerance for inexact evaluations; currently unused

  On return, \form#85, where

\(u \in \mathcal{C}^*\), \(v \in \mathcal{X}\), and \(\mathsf{ahuv} \in \mathcal{X}^*\).

The default implementation is a finite-difference approximation based on the adjoint Jacobian.

Reimplemented from ROL::Constraint< Real >.

Definition at line 85 of file ROL_LowerBoundToConstraint.hpp.

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