Defines the general constraint operator interface. More...

#include <ROL_Constraint.hpp>

Inheritance diagram for ROL::Constraint< Real >:

Public Member Functions
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	value (Vector< Real > &c, const Vector< Real > &x, Real &tol)=0
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...

virtual 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...

virtual 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...

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 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...

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)

Protected Member Functions
const std::vector< Real >	getParameter (void) const

Private Attributes
bool	activated_

std::vector< Real >	param_

Detailed Description

template<class Real>
class ROL::Constraint< Real >

Defines the general constraint operator interface.

ROL's constraint interface is designed for Fréchet differentiable operators \(c:\mathcal{X} \rightarrow \mathcal{C}\), where \(\mathcal{X}\) and \(\mathcal{C}\) are Banach spaces. The constraints are of the form

\[ c(x) = 0 \,. \]

The basic operator interface, to be implemented by the user, requires:

value – constraint evaluation.

It is strongly recommended that the user additionally overload:

applyJacobian – action of the constraint Jacobian –the default is a finite-difference approximation;
applyAdjointJacobian – action of the adjoint of the constraint Jacobian –the default is a finite-difference approximation.

The user may also overload:

applyAdjointHessian – action of the adjoint of the constraint Hessian –the default is a finite-difference approximation based on the adjoint Jacobian;
solveAugmentedSystem – solution of the augmented system –the default is an iterative scheme based on the action of the Jacobian and its adjoint.
applyPreconditioner – action of a constraint preconditioner –the default is null-op.

Definition at line 85 of file ROL_Constraint.hpp.

Constructor & Destructor Documentation

template<class Real>

virtual ROL::Constraint< Real >::~Constraint ( void )

inlinevirtual

Definition at line 90 of file ROL_Constraint.hpp.

template<class Real>

ROL::Constraint< Real >::Constraint ( void )

inline

Definition at line 92 of file ROL_Constraint.hpp.

Member Function Documentation

template<class Real>

virtual void ROL::Constraint< 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 in ROL::ROL::Constraint_SimOpt< Real >, ROL::Constraint_SimOpt< Real >, ROL::Reduced_Constraint_SimOpt< Real >, ROL::PrimalDualInteriorPointResidual< Real >, ROL::PrimalDualInteriorPointResidual< Real >, ROL::Constraint_Partitioned< Real >, ROL::LinearConstraint< Real >, ROL::ConstraintFromObjective< Real >, ROL::StochasticConstraint< Real >, ROL::Constraint_DynamicState< Real >, ROL::RiskNeutralConstraint< Real >, ROL::ROL::Constraint_State< Real >, ROL::Constraint_State< Real >, ROL::AlmostSureConstraint< Real >, ROL::SimulatedConstraint< Real >, and ROL::StdConstraint< Real >.

Definition at line 99 of file ROL_Constraint.hpp.

Referenced by ROL::CompositeStep< Real >::accept(), ROL::CompositeStep< Real >::initialize(), ROL::CompositeStep< Real >::update(), ROL::MoreauYosidaPenaltyStep< Real >::update(), and ROL::MoreauYosidaPenaltyStep< Real >::updateState().

template<class Real>

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

pure virtual

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 \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

Referenced by ROL::CompositeStep< Real >::accept(), ROL::CompositeStep< Real >::compute(), ROL::InteriorPointStep< Real >::initialize(), ROL::CompositeStep< Real >::initialize(), ROL::CompositeStep< Real >::update(), and ROL::MoreauYosidaPenaltyStep< Real >::updateState().

template<class Real >

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

virtual

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.

Definition at line 54 of file ROL_ConstraintDef.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::Vector< Real >::norm(), ROL::Vector< Real >::scale(), ROL::update(), ROL::value, and ROL::Vector< Real >::zero().

Referenced by ROL::CompositeStep< Real >::accept(), ROL::StdConstraint< Real >::applyJacobian(), ROL::CompositeStep< Real >::computeQuasinormalStep(), and ROL::CompositeStep< Real >::solveTangentialSubproblem().

template<class Real >

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

virtual

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.

Definition at line 87 of file ROL_ConstraintDef.hpp.

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

Referenced by ROL::CompositeStep< Real >::accept(), ROL::StdConstraint< Real >::applyAdjointJacobian(), ROL::CompositeStep< Real >::compute(), ROL::CompositeStep< Real >::computeLagrangeMultiplier(), ROL::CompositeStep< Real >::computeQuasinormalStep(), ROL::CompositeStep< Real >::initialize(), ROL::AugmentedLagrangianStep< Real >::initialize(), ROL::CompositeStep< Real >::update(), and ROL::MoreauYosidaPenaltyStep< Real >::updateState().

template<class Real >

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

virtual

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]       dualv  is a vector used for temporary variables; a constraint-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.

Definition at line 99 of file ROL_ConstraintDef.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::basis(), ROL::Vector< Real >::clone(), ROL::Vector< Real >::dimension(), ROL::Vector< Real >::dual(), ROL::Vector< Real >::norm(), ROL::update(), ROL::value, and ROL::Vector< Real >::zero().

template<class Real >

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

virtual

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.

Definition at line 166 of file ROL_ConstraintDef.hpp.

References ROL::Vector< Real >::axpy(), ROL::Vector< Real >::clone(), ROL::Vector< Real >::norm(), ROL::Vector< Real >::scale(), ROL::update(), and ROL::Vector< Real >::zero().

Referenced by ROL::CompositeStep< Real >::accept(), ROL::StdConstraint< Real >::applyAdjointHessian(), ROL::ZOO::Constraint_ParaboloidCircle< Real, XPrim, XDual, CPrim, CDual >::applyAdjointHessian(), ROL::Reduced_Constraint_SimOpt< Real >::applyAdjointHessian(), and ROL::CompositeStep< Real >::solveTangentialSubproblem().

template<class Real >

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

virtual

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 in ROL::ROL::Constraint_SimOpt< Real >, ROL::Constraint_SimOpt< Real >, Normalization_Constraint< Real >, ROL::StdConstraint< Real >, and ROL::ScalarLinearConstraint< Real >.

Definition at line 195 of file ROL_ConstraintDef.hpp.

References applyJacobian(), ROL::Vector< Real >::clone(), ROL::Vector< Real >::dot(), ROL::Vector< Real >::dual(), ROL::Vector< Real >::plus(), ROL::Objective_SerialSimOpt< Real >::zero, zero, and ROL::Vector< Real >::zero().

Referenced by ROL::CompositeStep< Real >::accept(), ROL::CompositeStep< Real >::computeLagrangeMultiplier(), ROL::CompositeStep< Real >::computeQuasinormalStep(), ROL::StdConstraint< Real >::solveAugmentedSystem(), Normalization_Constraint< Real >::solveAugmentedSystem(), ROL::Constraint_SimOpt< Real >::solveAugmentedSystem(), and ROL::CompositeStep< Real >::solveTangentialSubproblem().

template<class Real>

virtual void ROL::Constraint< 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.

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

  On return, \form#99, where

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

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

Reimplemented in ROL::ROL::Constraint_SimOpt< Real >, ROL::Constraint_SimOpt< Real >, ROL::SimulatedConstraint< Real >, ROL::Constraint_Partitioned< Real >, ROL::StdConstraint< Real >, ROL::AlmostSureConstraint< Real >, ROL::Constraint_DynamicState< Real >, ROL::ROL::Constraint_State< Real >, and ROL::Constraint_State< Real >.

Definition at line 269 of file ROL_Constraint.hpp.

References ROL::Vector< Real >::dual(), and ROL::Vector< Real >::set().

Referenced by ROL::StdConstraint< Real >::applyPreconditioner(), and ROL::Constraint_SimOpt< Real >::applyPreconditioner().

template<class Real>

void ROL::Constraint< Real >::activate ( void )

inline

Turn on constraints.

Definition at line 279 of file ROL_Constraint.hpp.

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

template<class Real>

void ROL::Constraint< Real >::deactivate ( void )

inline

Turn off constraints.

Definition at line 283 of file ROL_Constraint.hpp.

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

template<class Real>

bool ROL::Constraint< Real >::isActivated ( void )

inline

Check if constraints are on.

Definition at line 287 of file ROL_Constraint.hpp.

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

template<class Real >

std::vector< std::vector< Real > > ROL::Constraint< 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`
	)

virtual

Finite-difference check for the constraint Jacobian application.

Details here.

Definition at line 383 of file ROL_ConstraintDef.hpp.

References applyJacobian(), ROL::Vector< Real >::clone(), ROL::Finite_Difference_Arrays::shifts, ROL::update(), ROL::value, and ROL::Finite_Difference_Arrays::weights.

Referenced by main().

template<class Real >

std::vector< std::vector< Real > > ROL::Constraint< 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`
	)

virtual

Finite-difference check for the constraint Jacobian application.

Details here.

Definition at line 364 of file ROL_ConstraintDef.hpp.

template<class Real >

std::vector< std::vector< Real > > ROL::Constraint< 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`
	)

virtual

Finite-difference check for the application of the adjoint of constraint Jacobian.

Details here. (This function should be deprecated)

Definition at line 488 of file ROL_ConstraintDef.hpp.

References ROL::Vector< Real >::basis(), ROL::Vector< Real >::clone(), ROL::Vector< Real >::dimension(), ROL::Vector< Real >::dual(), ROL::update(), and ROL::value.

Referenced by main().

template<class Real>

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

inlinevirtual

Definition at line 340 of file ROL_Constraint.hpp.

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

Referenced by main().

template<class Real >

Real ROL::Constraint< 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

Definition at line 583 of file ROL_ConstraintDef.hpp.

References applyJacobian(), ROL::Vector< Real >::clone(), and ROL::Vector< Real >::dot().

template<class Real >

std::vector< std::vector< Real > > ROL::Constraint< 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`
	)

virtual

Finite-difference check for the application of the adjoint of constraint Hessian.

Details here.

Definition at line 634 of file ROL_ConstraintDef.hpp.

References ROL::Vector< Real >::clone(), ROL::Finite_Difference_Arrays::shifts, ROL::update(), and ROL::Finite_Difference_Arrays::weights.

Referenced by main().

template<class Real >

std::vector< std::vector< Real > > ROL::Constraint< 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`
	)