ROL::StdInequalityConstraint< Real > Class Template Reference

Provides a unique argument for inequality constraints using std::vector types, which otherwise behave exactly as equality constraints. More...

#include <ROL_StdInequalityConstraint.hpp>

Inheritance diagram for ROL::StdInequalityConstraint< Real >:

Public Member Functions
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...
void	value (V &c, const V &x, Real &tol)
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...
void	applyJacobian (V &jv, const V &v, const V &x, Real &tol)
	Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\). More...
void	applyAdjointJacobian (V &aju, const V &u, const V &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 (V &ahuv, const V &u, const V &v, const V &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...
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...
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...
Public Member Functions inherited from ROL::StdEqualityConstraint< Real >
virtual	~StdEqualityConstraint ()
virtual void	update (const std::vector< Real > &x, bool flag=true, int iter=-1)
virtual void	value (std::vector< Real > &c, const std::vector< Real > &x, Real &tol)=0
virtual void	applyJacobian (std::vector< Real > &jv, const std::vector< Real > v, const std::vector< Real > &x, Real &tol)
virtual void	applyAdjointJacobian (std::vector< Real > &ajv, const std::vector< Real > v, const std::vector< Real > &x, Real &tol)
virtual void	applyAdjointHessian (std::vector< Real > &ahuv, const std::vector< Real > &u, const std::vector< Real > &v, const std::vector< Real > &x, Real &tol)
virtual std::vector< Real >	solveAugmentedSystem (std::vector< Real > &v1, std::vector< Real > &v2, const std::vector< Real > &b1, const std::vector< Real > &b2, const std::vector< Real > &x, Real tol)
virtual void	applyPreconditioner (std::vector< Real > &pv, const std::vector< Real > &v, const std::vector< Real > &x, const std::vector< Real > &g, Real &tol)
Public Member Functions inherited from ROL::EqualityConstraint< Real >
virtual	~EqualityConstraint ()
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...
	EqualityConstraint (void)
virtual bool	isFeasible (const Vector< Real > &v)
	Check if the vector, v, is feasible. 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 Types
typedef StdEqualityConstraint < Real >	StdEC
typedef Vector< Real >	V

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

Detailed Description

template<class Real>
class ROL::StdInequalityConstraint< Real >

Provides a unique argument for inequality constraints using std::vector types, which otherwise behave exactly as equality constraints.

Definition at line 58 of file ROL_StdInequalityConstraint.hpp.

Member Typedef Documentation

template<class Real >

typedef StdEqualityConstraint<Real> ROL::StdInequalityConstraint< Real >::StdEC

private

Definition at line 61 of file ROL_StdInequalityConstraint.hpp.

template<class Real >

typedef Vector<Real> ROL::StdInequalityConstraint< Real >::V

private

Definition at line 62 of file ROL_StdInequalityConstraint.hpp.

Member Function Documentation

template<class Real >

void ROL::StdInequalityConstraint< Real >::update ( const Vector< Real > &  x, bool  flag = true, int  iter = -1  )

inlinevirtual

Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count.

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 67 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::update().

template<class Real >

void ROL::StdInequalityConstraint< Real >::value ( V &  c, const V &  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 \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

---

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 72 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::value().

template<class Real >

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

inlinevirtual

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

Parameters

[out]	jv	is the result of applying the constraint Jacobian to v at x; a constraint-space vector
[in]	v	is an optimization-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, \(\mathsf{jv} = c'(x)v\), where \(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).

The default implementation is a finite-difference approximation.

---

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 77 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::applyJacobian().

template<class Real >

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

inlinevirtual

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

Parameters

[out]	ajv	is the result of applying the adjoint of the constraint Jacobian to v at x; a dual optimization-space vector
[in]	v	is a dual 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, \(\mathsf{ajv} = c'(x)^*v\), where \(v \in \mathcal{C}^*\), \(\mathsf{ajv} \in \mathcal{X}^*\).

The default implementation is a finite-difference approximation.

---

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 82 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::applyAdjointJacobian().

template<class Real >

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

inlinevirtual

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

Parameters

[out]	ahuv	is the result of applying the derivative of the adjoint of the constraint Jacobian at x to vector u in direction v; a dual optimization-space vector
[in]	u	is the direction vector; a dual constraint-space vector
[in]	v	is an optimization-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, \( \mathsf{ahuv} = c''(x)(v,\cdot)^*u \), 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::StdEqualityConstraint< Real >.

Definition at line 87 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::applyAdjointHessian().

template<class Real >

std::vector<Real> ROL::StdInequalityConstraint< Real >::solveAugmentedSystem ( Vector< Real > &  v1, Vector< Real > &  v2, const Vector< Real > &  b1, const Vector< Real > &  b2, const Vector< Real > &  x, Real &  tol  )

inlinevirtual

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.

Parameters

[out]	v1	is the optimization-space component of the result
[out]	v2	is the dual constraint-space component of the result
[in]	b1	is the dual optimization-space component of the right-hand side
[in]	b2	is the constraint-space component of the right-hand side
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is the nominal relative residual tolerance

On return, \( [\mathsf{v1} \,\, \mathsf{v2}] \) approximately solves the augmented system, where the size of the residual is governed by special stopping conditions.

The default implementation is the preconditioned generalized minimal residual (GMRES) method, which enables the use of nonsymmetric preconditioners.

---

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 93 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::solveAugmentedSystem().

template<class Real >

void ROL::StdInequalityConstraint< Real >::applyPreconditioner ( Vector< Real > &  pv, const Vector< Real > &  v, const Vector< Real > &  x, const Vector< Real > &  g, Real &  tol  )

inlinevirtual

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.

Parameters

[out]	pv	is the result of applying the constraint preconditioner to v at x; a dual constraint-space vector
[in]	v	is a constraint-space vector
[in]	x	is the preconditioner argument; an optimization-space vector
[in]	g	is the preconditioner argument; a dual optimization-space vector, unused
[in,out]	tol	is a tolerance for inexact evaluations

On return, \(\mathsf{pv} = P(x)v\), where \(v \in \mathcal{C}\), \(\mathsf{pv} \in \mathcal{C}^*\).

The default implementation is the Riesz map in \(L(\mathcal{C}, \mathcal{C}^*)\).

---

Reimplemented from ROL::StdEqualityConstraint< Real >.

Definition at line 100 of file ROL_StdInequalityConstraint.hpp.

References ROL::StdEqualityConstraint< Real >::applyPreconditioner().

---

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

• ROL_StdInequalityConstraint.hpp