ROL::ROL::Objective< Real > Class Template Reference

#include <ROL_Constraint_SerialSimOpt.hpp>

Inheritance diagram for ROL::ROL::Objective< Real >:

Public Member Functions
virtual	~Objective ()
	Objective ()
virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update objective function.
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function.
virtual Real	value (const Vector< Real > &x, Real &tol)=0
	Compute value.
virtual void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
	Compute gradient.
virtual Real	dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol)
	Compute directional derivative.
virtual void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply Hessian approximation to vector.
virtual void	invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply inverse Hessian approximation to vector.
virtual void	precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply preconditioner to vector.
virtual std::vector< std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference gradient check.
virtual std::vector< std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference gradient check.
virtual std::vector< std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference gradient check with specified step sizes.
virtual std::vector< std::vector< Real > >	checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference gradient check with specified step sizes.
virtual std::vector< std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference Hessian-applied-to-vector check.
virtual std::vector< std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference Hessian-applied-to-vector check.
virtual std::vector< std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference Hessian-applied-to-vector check with specified step sizes.
virtual std::vector< std::vector< Real > >	checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference Hessian-applied-to-vector check with specified step sizes.
virtual std::vector< Real >	checkHessSym (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
	Hessian symmetry check.
virtual std::vector< Real >	checkHessSym (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
	Hessian symmetry check.
virtual void	setParameter (const std::vector< Real > &param)

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

Private Attributes
Ptr< Vector< Real > >	prim_
Ptr< Vector< Real > >	dual_
Ptr< Vector< Real > >	basis_
std::vector< Real >	param_

Detailed Description

template<typename Real>
class ROL::ROL::Objective< Real >

Definition at line 78 of file ROL_Constraint_SerialSimOpt.hpp.

Constructor & Destructor Documentation

~Objective()

template<typename Real>

virtual ROL::ROL::Objective< Real >::~Objective ( )

inlinevirtual

Definition at line 85 of file ROL_Constraint_SerialSimOpt.hpp.

Objective()

template<typename Real>

ROL::ROL::Objective< Real >::Objective ( )

inline

Definition at line 87 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::ROL::AffineTransformObjective< Real >::AffineTransformObjective(), ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangianObjective< Real >::AugmentedLagrangianObjective(), ROL::AugmentedLagrangianObjective< Real >::AugmentedLagrangianObjective(), ROL::CDFObjective< Real >::CDFObjective(), ROL::CompositeObjective< Real >::CompositeObjective(), ROL::ElasticObjective< Real >::ElasticObjective(), ROL::ElasticObjective< Real >::ElasticObjective(), ROL::FletcherBase< Real >::FletcherBase(), ROL::FletcherObjectiveBase< Real >::FletcherObjectiveBase(), ROL::InteriorPointObjective< Real >::InteriorPointObjective(), ROL::InteriorPointObjective< Real >::InteriorPointObjective(), ROL::InteriorPointPenalty< Real >::InteriorPointPenalty(), ROL::LinearCombinationObjective< Real >::LinearCombinationObjective(), ROL::LinearCombinationObjective< Real >::LinearCombinationObjective(), ROL::MeanValueObjective< Real >::MeanValueObjective(), ROL::MomentObjective< Real >::MomentObjective(), ROL::MomentObjective< Real >::MomentObjective(), ROL::MoreauYosidaObjective< Real >::MoreauYosidaObjective(), ROL::MoreauYosidaObjective< Real >::MoreauYosidaObjective(), ROL::MoreauYosidaObjective< Real >::MoreauYosidaObjective(), ROL::MoreauYosidaObjective< Real >::MoreauYosidaObjective(), ROL::MoreauYosidaPenalty< Real >::MoreauYosidaPenalty(), ROL::MoreauYosidaPenalty< Real >::MoreauYosidaPenalty(), ROL::MoreauYosidaPenalty< Real >::MoreauYosidaPenalty(), ROL::ObjectiveMMA< Real >::ObjectiveMMA(), ROL::InteriorPoint::PenalizedObjective< Real >::PenalizedObjective(), ROL::PH_bPOEObjective< Real >::PH_bPOEObjective(), ROL::PH_DeviationObjective< Real >::PH_DeviationObjective(), ROL::PH_ErrorObjective< Real >::PH_ErrorObjective(), ROL::PH_Objective< Real >::PH_Objective(), ROL::PH_ProbObjective< Real >::PH_ProbObjective(), ROL::PH_RegretObjective< Real >::PH_RegretObjective(), ROL::PH_RiskObjective< Real >::PH_RiskObjective(), ROL::PointwiseCDFObjective< Real >::PointwiseCDFObjective(), ROL::ProjectedObjective< Real >::ProjectedObjective(), ROL::RiskLessObjective< Real >::RiskLessObjective(), ROL::RiskNeutralObjective< Real >::RiskNeutralObjective(), ROL::RiskNeutralObjective< Real >::RiskNeutralObjective(), ROL::RiskNeutralObjective< Real >::RiskNeutralObjective(), ROL::ScaledObjective< Real >::ScaledObjective(), ROL::TrustRegionModel_U< Real >::setData(), ROL::SlacklessObjective< Real >::SlacklessObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::StochasticObjective< Real >::StochasticObjective(), ROL::TrustRegionModel< Real >::TrustRegionModel(), ROL::TrustRegionModel< Real >::update(), ROL::TrustRegionModel_U< Real >::validate(), and ROL::StdObjective< Real >::value().

Member Function Documentation

update() [1/2]

template<typename Real>

virtual void ROL::ROL::Objective< Real >::update ( const Vector< Real > & x, UpdateType type, int iter = -1 )

inlinevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters

[in]	x	is the new iterate.
[in]	type	is the type of update requested.
[in]	iter	is the outer algorithm iterations count.

Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, and ROL::ROL::NonlinearLeastSquaresObjective< Real >.

Definition at line 96 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), and ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run().

update() [2/2]

template<typename Real>

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

inlinevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters

[in]	x	is the new iterate.
[in]	flag	is true if the iterate has changed.
[in]	iter	is the outer algorithm iterations count.

Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, and ROL::ROL::QuadraticPenalty< Real >.

Definition at line 109 of file ROL_Constraint_SerialSimOpt.hpp.

value()

template<typename Real>

virtual Real ROL::ROL::Objective< Real >::value ( const Vector< Real > & x, Real & tol )

pure virtual

Compute value.

This function returns the objective function value.

Parameters

[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

Implemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.

Referenced by ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run(), and ROL::FletcherStep< Real >::update().

gradient()

template<typename Real>

void ROL::ROL::Objective< Real >::gradient ( Vector< Real > & g, const Vector< Real > & x, Real & tol )

virtual

Compute gradient.

This function returns the objective function gradient.

Parameters

[out]	g	is the gradient.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

The default implementation is a finite-difference approximation based on the function value. This requires the definition of a basis \(\{\phi_i\}\) for the optimization vectors x and the definition of a basis \(\{\psi_j\}\) for the dual optimization vectors (gradient vectors g). The bases must be related through the Riesz map, i.e., \( R \{\phi_i\} = \{\psi_j\}\), and this must be reflected in the implementation of the ROL::Vector::dual() method.

Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.

Definition at line 74 of file ROL_ObjectiveDef.hpp.

References ROL::ROL::Vector< Real >::axpy(), ROL::ROL::Vector< Real >::basis(), basis_, ROL::ROL::Vector< Real >::clone(), ROL::ROL::Vector< Real >::dimension(), ROL::ROL::Vector< Real >::dot(), prim_, ROL::ROL::Revert, ROL::ROL::ROL_EPSILON(), ROL::ROL::Temp, ROL::update(), ROL::value(), ROL::ROL::Vector< Real >::zero(), and zero.

Referenced by checkGradient(), checkHessVec(), dirDeriv(), ROL::FletcherBase< Real >::getGradient(), ROL::FletcherObjectiveBase< Real >::getGradient(), hessVec(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run(), and ROL::FletcherStep< Real >::update().

dirDeriv()

template<typename Real>

Real ROL::ROL::Objective< Real >::dirDeriv ( const Vector< Real > & x, const Vector< Real > & d, Real & tol )

virtual

Compute directional derivative.

This function returns the directional derivative of the objective function in the \(d\) direction.

Parameters

[in]	x	is the current iterate.
[in]	d	is the direction.
[in]	tol	is a tolerance for inexact objective function computation.

Definition at line 54 of file ROL_ObjectiveDef.hpp.

References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), ROL::ROL::Vector< Real >::dual(), dual_, and gradient().

hessVec()

template<typename Real>

void ROL::ROL::Objective< Real >::hessVec ( Vector< Real > & hv, const Vector< Real > & v, const Vector< Real > & x, Real & tol )

virtual

Apply Hessian approximation to vector.

This function applies the Hessian of the objective function to the vector \(v\).

Parameters

[out]	hv	is the the action of the Hessian on \(v\).
[in]	v	is the direction vector.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.

Definition at line 95 of file ROL_ObjectiveDef.hpp.

References ROL::ROL::Vector< Real >::axpy(), ROL::ROL::Vector< Real >::clone(), dual_, gradient(), ROL::ROL::Vector< Real >::norm(), prim_, ROL::ROL::Revert, ROL::ROL::Vector< Real >::scale(), ROL::ROL::Temp, ROL::update(), ROL::ROL::Vector< Real >::zero(), and zero.

Referenced by checkHessSym(), checkHessVec(), ROL::ZOO::Objective_DiodeCircuit< Real >::hessVec(), and main().

invHessVec()

template<typename Real>

virtual void ROL::ROL::Objective< Real >::invHessVec ( Vector< Real > & hv, const Vector< Real > & v, const Vector< Real > & x, Real & tol )

inlinevirtual

Apply inverse Hessian approximation to vector.

This function applies the inverse Hessian of the objective function to the vector \(v\).

Parameters

[out]	hv	is the action of the inverse Hessian on \(v\).
[in]	v	is the direction vector.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

Reimplemented in ROL::ROL::TrustRegionModel_U< Real >.

Definition at line 165 of file ROL_Constraint_SerialSimOpt.hpp.

precond()

template<typename Real>

virtual void ROL::ROL::Objective< Real >::precond ( Vector< Real > & Pv, const Vector< Real > & v, const Vector< Real > & x, Real & tol )

inlinevirtual

Apply preconditioner to vector.

This function applies a preconditioner for the Hessian of the objective function to the vector \(v\).

Parameters

[out]	Pv	is the action of the Hessian preconditioner on \(v\).
[in]	v	is the direction vector.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.

Reimplemented in ROL::ROL::NonlinearLeastSquaresObjective< Real >, and ROL::ROL::TrustRegionModel_U< Real >.

Definition at line 183 of file ROL_Constraint_SerialSimOpt.hpp.

checkGradient() [1/4]

template<typename Real>

virtual std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkGradient ( const Vector< Real > & x, const Vector< Real > & d, const bool printToStream = true, std::ostream & outStream = std::cout, const int numSteps = ROL_NUM_CHECKDERIV_STEPS, const int order = 1 )

inlinevirtual

Finite-difference gradient check.

This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	d	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	numSteps	is a parameter which dictates the number of finite difference steps.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 209 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by checkGradient(), and main().

checkGradient() [2/4]

template<typename Real>

std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkGradient ( const Vector< Real > & x, const Vector< Real > & g, const Vector< Real > & d, const bool printToStream = true, std::ostream & outStream = std::cout, const int numSteps = ROL_NUM_CHECKDERIV_STEPS, const int order = 1 )

virtual

Finite-difference gradient check.

This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	g	is used to create a temporary gradient vector.
[in]	d	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	numSteps	is a parameter which dictates the number of finite difference steps.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 119 of file ROL_ObjectiveDef.hpp.

References checkGradient().

checkGradient() [3/4]

template<typename Real>

virtual std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkGradient ( const Vector< Real > & x, const Vector< Real > & d, const std::vector< Real > & steps, const bool printToStream = true, std::ostream & outStream = std::cout, const int order = 1 )

inlinevirtual

Finite-difference gradient check with specified step sizes.

This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	d	is a direction vector.
[in]	steps	is vector of steps of user-specified size.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 269 of file ROL_Constraint_SerialSimOpt.hpp.

checkGradient() [4/4]

template<typename Real>

std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkGradient ( const Vector< Real > & x, const Vector< Real > & g, const Vector< Real > & d, const std::vector< Real > & steps, const bool printToStream = true, std::ostream & outStream = std::cout, const int order = 1 )

virtual

Finite-difference gradient check with specified step sizes.

This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	g	is used to create a temporary gradient vector.
[in]	d	is a direction vector.
[in]	steps	is vector of steps of user-specified size.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 138 of file ROL_ObjectiveDef.hpp.

References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), gradient(), ROL::ROL::ROL_EPSILON(), ROL::ROL::Finite_Difference_Arrays::shifts, ROL::ROL::Temp, ROL::update(), ROL::value(), and ROL::ROL::Finite_Difference_Arrays::weights.

checkHessVec() [1/4]

template<typename Real>

virtual std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkHessVec ( const Vector< Real > & x, const Vector< Real > & v, const bool printToStream = true, std::ostream & outStream = std::cout, const int numSteps = ROL_NUM_CHECKDERIV_STEPS, const int order = 1 )

inlinevirtual

Finite-difference Hessian-applied-to-vector check.

This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	v	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	numSteps	is a parameter which dictates the number of finite difference steps.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 331 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by checkHessVec(), and main().

checkHessVec() [2/4]

template<typename Real>

std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkHessVec ( const Vector< Real > & x, const Vector< Real > & hv, const Vector< Real > & v, const bool printToStream = true, std::ostream & outStream = std::cout, const int numSteps = ROL_NUM_CHECKDERIV_STEPS, const int order = 1 )

virtual

Finite-difference Hessian-applied-to-vector check.

This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	hv	is used to create temporary gradient and Hessian-times-vector vectors.
[in]	v	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	numSteps	is a parameter which dictates the number of finite difference steps.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 234 of file ROL_ObjectiveDef.hpp.

References checkHessVec().

checkHessVec() [3/4]

template<typename Real>

virtual std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkHessVec ( const Vector< Real > & x, const Vector< Real > & v, const std::vector< Real > & steps, const bool printToStream = true, std::ostream & outStream = std::cout, const int order = 1 )

inlinevirtual

Finite-difference Hessian-applied-to-vector check with specified step sizes.

This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	v	is a direction vector.
[in]	steps	is vector of steps of user-specified size.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 392 of file ROL_Constraint_SerialSimOpt.hpp.

checkHessVec() [4/4]

template<typename Real>

std::vector< std::vector< Real > > ROL::ROL::Objective< Real >::checkHessVec ( const Vector< Real > & x, const Vector< Real > & hv, const Vector< Real > & v, const std::vector< Real > & steps, const bool printToStream = true, std::ostream & outStream = std::cout, const int order = 1 )

virtual

Finite-difference Hessian-applied-to-vector check with specified step sizes.

This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error

\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]

if the approximation is first order. More generally, difference approximation is

\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]

where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps

Parameters

[in]	x	is an optimization variable.
[in]	hv	is used to create temporary gradient and Hessian-times-vector vectors.
[in]	v	is a direction vector.
[in]	steps	is vector of steps of user-specified size.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.
[in]	order	is the order of the finite difference approximation (1,2,3,4)

Definition at line 253 of file ROL_ObjectiveDef.hpp.

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

checkHessSym() [1/2]

template<typename Real>

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

inlinevirtual

Hessian symmetry check.

This function checks the symmetry of the Hessian by comparing

\[ \langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}} \quad\text{and}\quad \langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}. \]

Parameters

[in]	x	is an optimization variable.
[in]	v	is a direction vector.
[in]	w	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.

Definition at line 447 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by main().

checkHessSym() [2/2]

template<typename Real>

std::vector< Real > ROL::ROL::Objective< Real >::checkHessSym ( const Vector< Real > & x, const Vector< Real > & hv, const Vector< Real > & v, const Vector< Real > & w, const bool printToStream = true, std::ostream & outStream = std::cout )

virtual

Hessian symmetry check.

This function checks the symmetry of the Hessian by comparing

\[ \langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}} \quad\text{and}\quad \langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}. \]

Parameters

[in]	x	is an optimization variable.
[in]	hv	is used to create temporary Hessian-times-vector vectors.
[in]	v	is a direction vector.
[in]	w	is a direction vector.
[in]	printToStream	is a flag that turns on/off output.
[out]	outStream	is the output stream.

Definition at line 350 of file ROL_ObjectiveDef.hpp.

References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), hessVec(), ROL::ROL::ROL_EPSILON(), ROL::ROL::Temp, and ROL::update().

getParameter()

template<typename Real>

const std::vector< Real > ROL::ROL::Objective< Real >::getParameter ( void ) const

inlineprotected

Definition at line 484 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by DiffusionObjective< Real >::gradient_1(), DiffusionObjective< Real >::hessVec_11(), ROL::ROL::AffineTransformObjective< Real >::transform(), and DiffusionObjective< Real >::value().

setParameter()

template<typename Real>

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

inlinevirtual

Reimplemented in ROL::AffineTransformObjective< Real >, ROL::CompositeObjective< Real >, ROL::CompositeObjective_SimOpt< Real >, ROL::LinearCombinationObjective< Real >, ROL::LinearCombinationObjective_SimOpt< Real >, ROL::MoreauYosidaPenalty< Real >, ROL::NonlinearLeastSquaresObjective< Real >, ROL::PH_bPOEObjective< Real >, ROL::PH_DeviationObjective< Real >, ROL::PH_ErrorObjective< Real >, ROL::PH_Objective< Real >, ROL::PH_ProbObjective< Real >, ROL::PH_RegretObjective< Real >, ROL::PH_RiskObjective< Real >, ROL::Reduced_AugmentedLagrangian_SimOpt< Real >, ROL::Reduced_Objective_SimOpt< Real >, ROL::RiskLessObjective< Real >, ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ScaledObjective< Real >, and ROL::SlacklessObjective< Real >.

Definition at line 489 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by ROL::CompositeObjective_SimOpt< Real >::setParameter(), ROL::LinearCombinationObjective_SimOpt< Real >::setParameter(), and ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::setParameter().

Member Data Documentation

prim_

template<typename Real>

Ptr<Vector<Real> > ROL::ROL::Objective< Real >::prim_

private

Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by gradient(), and hessVec().

dual_

template<typename Real>

Ptr<Vector<Real> > ROL::ROL::Objective< Real >::dual_

private

Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by dirDeriv(), and hessVec().

basis_

template<typename Real>

Ptr<Vector<Real> > ROL::ROL::Objective< Real >::basis_

private

Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.

Referenced by gradient().

param_

template<typename Real>

std::vector<Real> ROL::ROL::Objective< Real >::param_

private

Definition at line 481 of file ROL_Constraint_SerialSimOpt.hpp.

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

• ROL_Constraint_SerialSimOpt.hpp
• ROL_ObjectiveDef.hpp