ROL::Objective< Real > Class Template Reference

Provides the interface to evaluate objective functions. More...

#include <ROL_Objective.hpp>

Inheritance diagram for 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 void	prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
	Compute the proximity operator.
virtual void	proxJacVec (Vector< Real > &Jv, const Vector< Real > &v, const Vector< Real > &x, Real t, Real &tol)
	Apply the Jacobian of the proximity operator.
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 std::vector< std::vector< Real > >	checkProxJacVec (const Vector< Real > &x, const Vector< Real > &v, Real t=Real(1), bool printToStream=true, std::ostream &outStream=std::cout, int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference proximity operator Jacobian-applied-to-vector 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::Objective< Real >

Provides the interface to evaluate objective functions.

Provides the definition of the objective function interface.

ROL's objective function interface is designed for Fr$eacute;chet differentiable functionals \(f:\mathcal{X}\to\mathbb{R}\), where \(\mathcal{X}\) is a Banach space. The basic operator interace, to be implemented by the user, requires:

• value – objective function evaluation.

It is strongly recommended that the user additionally overload:

• gradient – the objective function gradient – the default is a finite-difference approximation;
• hessVec – the action of the Hessian – the default is a finite-difference approximation.

The user may also overload:

• update – update the objective function at each new iteration;
• dirDeriv – compute the directional derivative – the default is a finite-difference approximation;
• invHessVec – the action of the inverse Hessian;
• precond – the action of a preconditioner for the Hessian.

---

Definition at line 44 of file ROL_Objective.hpp.

Constructor & Destructor Documentation

~Objective()

template<typename Real>

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

inlinevirtual

Definition at line 51 of file ROL_Objective.hpp.

Objective()

template<typename Real>

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

inline

Definition at line 53 of file ROL_Objective.hpp.

References basis_, dual_, and prim_.

Member Function Documentation

update() [1/2]

template<typename Real>

virtual void 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.

Definition at line 62 of file ROL_Objective.hpp.

References ROL_UNUSED.

Referenced by ROL::CompositeStep< Real >::accept(), ROL::BundleStep< Real >::compute(), ROL::TypeB::LinMoreAlgorithm< Real >::computeValue(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::computeValue(), ROL::TypeP::TrustRegionAlgorithm< Real >::computeValue(), ROL::TypeP::TrustRegionAlgorithm< Real >::dbls(), ROL::TypeP::TrustRegionAlgorithm< Real >::dcauchy(), ROL::LineSearch_U< Real >::dirDeriv(), ROL::TypeP::TrustRegionAlgorithm< Real >::dncg(), ROL::TypeP::TrustRegionAlgorithm< Real >::dspg(), ROL::TypeP::TrustRegionAlgorithm< Real >::dspg2(), ROL::TypeB::LSecantBAlgorithm< Real >::dsrch(), ROL::LineSearch< Real >::getInitialAlpha(), ROL::LineSearch_U< Real >::getInitialAlpha(), ROL::CompositeStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::PrimalDualActiveSetStep< Real >::initialize(), ROL::Step< Real >::initialize(), ROL::TrustRegionStep< Real >::initialize(), ROL::TypeB::ColemanLiAlgorithm< Real >::initialize(), ROL::TypeB::GradientAlgorithm< Real >::initialize(), ROL::TypeB::KelleySachsAlgorithm< Real >::initialize(), ROL::TypeB::LinMoreAlgorithm< Real >::initialize(), ROL::TypeB::LSecantBAlgorithm< Real >::initialize(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::initialize(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::initialize(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeB::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::initialize(), ROL::TypeP::InexactNewtonAlgorithm< Real >::initialize(), ROL::TypeP::iPianoAlgorithm< Real >::initialize(), ROL::TypeP::ProxGradientAlgorithm< Real >::initialize(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeP::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeP::TrustRegionAlgorithm< Real >::initialize(), ROL::TypeU::BundleAlgorithm< Real >::initialize(), ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::TRUtils::initialRadius(), ROL::BackTracking< Real >::run(), ROL::BackTracking_U< Real >::run(), ROL::Bisection< Real >::run(), ROL::CubicInterp< Real >::run(), ROL::CubicInterp_U< Real >::run(), ROL::GoldenSection< Real >::run(), ROL::IterationScaling< Real >::run(), ROL::IterationScaling_U< Real >::run(), ROL::PathBasedTargetLevel< Real >::run(), ROL::PathBasedTargetLevel_U< Real >::run(), ROL::TypeB::ColemanLiAlgorithm< Real >::run(), ROL::TypeB::GradientAlgorithm< Real >::run(), ROL::TypeB::KelleySachsAlgorithm< Real >::run(), ROL::TypeB::LinMoreAlgorithm< Real >::run(), ROL::TypeB::LSecantBAlgorithm< Real >::run(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::run(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::run(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeB::SpectralGradientAlgorithm< Real >::run(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::run(), ROL::TypeP::InexactNewtonAlgorithm< Real >::run(), ROL::TypeP::iPianoAlgorithm< Real >::run(), ROL::TypeP::ProxGradientAlgorithm< Real >::run(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeP::SpectralGradientAlgorithm< Real >::run(), ROL::TypeP::TrustRegionAlgorithm< Real >::run(), ROL::TypeU::BundleAlgorithm< Real >::run(), ROL::TypeU::LineSearchAlgorithm< Real >::run(), ROL::LineSearch< Real >::status(), ROL::AugmentedLagrangianStep< Real >::update(), ROL::CompositeStep< Real >::update(), ROL::GradientStep< Real >::update(), ROL::NewtonKrylovStep< Real >::update(), ROL::NewtonStep< Real >::update(), ROL::NonlinearCGStep< Real >::update(), ROL::PrimalDualActiveSetStep< Real >::update(), ROL::ProjectedNewtonKrylovStep< Real >::update(), ROL::ProjectedNewtonStep< Real >::update(), ROL::ProjectedSecantStep< Real >::update(), ROL::SecantStep< Real >::update(), and ROL::TrustRegion< Real >::update().

update() [2/2]

template<typename Real>

virtual void 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 CLExactModel< Real >, and Objective_PoissonInversion< Real >.

Definition at line 75 of file ROL_Objective.hpp.

References ROL_UNUSED.

value()

template<typename Real>

virtual Real 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 CLExactModel< Real >, CLTestObjective< Real >, NullObjective< Real >, Objective_BurgersControl< Real >, Objective_GrossPitaevskii< Real >, Objective_GrossPitaevskii< Real >, Objective_PoissonInversion< Real >, and Zakharov_Sacado_Objective< Real >.

Referenced by ROL::CompositeStep< Real >::accept(), ROL::BundleStep< Real >::compute(), ROL::CompositeStep< Real >::compute(), ROL::TypeB::LinMoreAlgorithm< Real >::computeValue(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::computeValue(), ROL::TypeP::TrustRegionAlgorithm< Real >::computeValue(), ROL::TypeP::TrustRegionAlgorithm< Real >::dbls(), ROL::TypeP::TrustRegionAlgorithm< Real >::dcauchy(), ROL::LineSearch_U< Real >::dirDeriv(), ROL::TypeP::TrustRegionAlgorithm< Real >::dncg(), ROL::TypeP::TrustRegionAlgorithm< Real >::dspg(), ROL::TypeP::TrustRegionAlgorithm< Real >::dspg2(), ROL::TypeB::LSecantBAlgorithm< Real >::dsrch(), ROL::LineSearch< Real >::getInitialAlpha(), ROL::LineSearch_U< Real >::getInitialAlpha(), ROL::CompositeStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::PrimalDualActiveSetStep< Real >::initialize(), ROL::Step< Real >::initialize(), ROL::TrustRegionStep< Real >::initialize(), ROL::TypeB::ColemanLiAlgorithm< Real >::initialize(), ROL::TypeB::GradientAlgorithm< Real >::initialize(), ROL::TypeB::KelleySachsAlgorithm< Real >::initialize(), ROL::TypeB::LinMoreAlgorithm< Real >::initialize(), ROL::TypeB::LSecantBAlgorithm< Real >::initialize(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::initialize(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::initialize(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeB::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::initialize(), ROL::TypeP::InexactNewtonAlgorithm< Real >::initialize(), ROL::TypeP::iPianoAlgorithm< Real >::initialize(), ROL::TypeP::ProxGradientAlgorithm< Real >::initialize(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeP::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeP::TrustRegionAlgorithm< Real >::initialize(), ROL::TypeU::BundleAlgorithm< Real >::initialize(), ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::TRUtils::initialRadius(), ROL::BackTracking< Real >::run(), ROL::BackTracking_U< Real >::run(), ROL::Bisection< Real >::run(), ROL::CubicInterp< Real >::run(), ROL::CubicInterp_U< Real >::run(), ROL::GoldenSection< Real >::run(), ROL::IterationScaling< Real >::run(), ROL::IterationScaling_U< Real >::run(), ROL::PathBasedTargetLevel< Real >::run(), ROL::PathBasedTargetLevel_U< Real >::run(), ROL::TypeB::ColemanLiAlgorithm< Real >::run(), ROL::TypeB::GradientAlgorithm< Real >::run(), ROL::TypeB::KelleySachsAlgorithm< Real >::run(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::run(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::run(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeB::SpectralGradientAlgorithm< Real >::run(), ROL::TypeP::InexactNewtonAlgorithm< Real >::run(), ROL::TypeP::iPianoAlgorithm< Real >::run(), ROL::TypeP::ProxGradientAlgorithm< Real >::run(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeP::SpectralGradientAlgorithm< Real >::run(), ROL::TypeU::BundleAlgorithm< Real >::run(), ROL::TypeU::LineSearchAlgorithm< Real >::run(), ROL::CompositeStep< Real >::update(), ROL::GradientStep< Real >::update(), ROL::NewtonKrylovStep< Real >::update(), ROL::NewtonStep< Real >::update(), ROL::NonlinearCGStep< Real >::update(), ROL::PrimalDualActiveSetStep< Real >::update(), ROL::ProjectedNewtonKrylovStep< Real >::update(), ROL::ProjectedNewtonStep< Real >::update(), ROL::ProjectedSecantStep< Real >::update(), ROL::SecantStep< Real >::update(), and ROL::TrustRegion< Real >::update().

gradient()

template<typename Real>

virtual void 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 CLExactModel< Real >, CLTestObjective< Real >, NullObjective< Real >, Objective_BurgersControl< Real >, Objective_GrossPitaevskii< Real >, Objective_GrossPitaevskii< Real >, Objective_PoissonInversion< Real >, and Zakharov_Sacado_Objective< Real >.

Referenced by ROL::CompositeStep< Real >::accept(), ROL::BundleStep< Real >::compute(), ROL::CompositeStep< Real >::compute(), ROL::PrimalDualActiveSetStep< Real >::computeCriticalityMeasure(), ROL::TypeB::LinMoreAlgorithm< Real >::computeGradient(), ROL::TypeB::TrustRegionSPGAlgorithm< Real >::computeGradient(), ROL::TypeP::TrustRegionAlgorithm< Real >::computeGradient(), ROL::CompositeStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::InteriorPointStep< Real >::initialize(), ROL::Step< Real >::initialize(), ROL::TypeB::ColemanLiAlgorithm< Real >::initialize(), ROL::TypeB::GradientAlgorithm< Real >::initialize(), ROL::TypeB::KelleySachsAlgorithm< Real >::initialize(), ROL::TypeB::LSecantBAlgorithm< Real >::initialize(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::initialize(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::initialize(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeB::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeP::InexactNewtonAlgorithm< Real >::initialize(), ROL::TypeP::iPianoAlgorithm< Real >::initialize(), ROL::TypeP::ProxGradientAlgorithm< Real >::initialize(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeP::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeU::BundleAlgorithm< Real >::initialize(), ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::TypeB::ColemanLiAlgorithm< Real >::run(), ROL::TypeB::GradientAlgorithm< Real >::run(), ROL::TypeB::KelleySachsAlgorithm< Real >::run(), ROL::TypeB::LSecantBAlgorithm< Real >::run(), ROL::TypeB::NewtonKrylovAlgorithm< Real >::run(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::run(), ROL::TypeB::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeB::SpectralGradientAlgorithm< Real >::run(), ROL::TypeP::InexactNewtonAlgorithm< Real >::run(), ROL::TypeP::iPianoAlgorithm< Real >::run(), ROL::TypeP::ProxGradientAlgorithm< Real >::run(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::run(), ROL::TypeP::SpectralGradientAlgorithm< Real >::run(), ROL::TypeU::BundleAlgorithm< Real >::run(), ROL::TypeU::LineSearchAlgorithm< Real >::run(), ROL::LineSearch< Real >::status(), ROL::CompositeStep< Real >::update(), ROL::GradientStep< Real >::update(), ROL::NewtonKrylovStep< Real >::update(), ROL::NewtonStep< Real >::update(), ROL::NonlinearCGStep< Real >::update(), ROL::ProjectedNewtonKrylovStep< Real >::update(), ROL::ProjectedNewtonStep< Real >::update(), ROL::ProjectedSecantStep< Real >::update(), ROL::SecantStep< Real >::update(), ROL::TrustRegion< Real >::update(), and ROL::TrustRegionStep< Real >::updateGradient().

dirDeriv()

template<typename Real>

virtual Real 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.

Referenced by ROL::LineSearch_U< Real >::dirDeriv(), and ROL::StdObjective< Real >::dirDeriv().

hessVec()

template<typename Real>

virtual void 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 CLExactModel< Real >, CLTestObjective< Real >, NullObjective< Real >, Objective_BurgersControl< Real >, Objective_GrossPitaevskii< Real >, Objective_GrossPitaevskii< Real >, Objective_PoissonInversion< Real >, and Zakharov_Sacado_Objective< Real >.

Referenced by ROL::CompositeStep< Real >::accept(), ROL::PrimalDualActiveSetStep< Real >::compute(), ROL::computeDenseHessian(), ROL::computeScaledDenseHessian(), ROL::Reduced_Objective_SimOpt< Real >::hessVec(), ROL::ReducedDynamicObjective< Real >::hessVec(), ROL::StdObjective< Real >::hessVec(), ROL::ZOO::Objective_DiodeCircuit< Real >::hessVec(), ROL::TrustRegionStep< Real >::initialize(), ROL::TypeB::PrimalDualActiveSetAlgorithm< Real >::run(), and ROL::CompositeStep< Real >::solveTangentialSubproblem().

invHessVec()

template<typename Real>

virtual void 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.

Definition at line 131 of file ROL_Objective.hpp.

References ROL_UNUSED.

Referenced by ROL::Newton_U< Real >::compute(), ROL::NewtonStep< Real >::compute(), ROL::ProjectedNewtonStep< Real >::compute(), ROL::TrustRegionStep< Real >::initialize(), and ROL::TrustRegionModel_U< Real >::validate().

precond()

template<typename Real>

virtual void 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.

Definition at line 149 of file ROL_Objective.hpp.

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

prox()

template<typename Real>

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

inlinevirtual

Compute the proximity operator.

This function returns the proximity operator.

Parameters

[out]	Pv	is the proximity operator applied to \(v\) (primal optimization vector).
[in]	v	is the input to the proximity operator (primal optimization vector).
[in]	t	is the proximity operator parameter (positive scalar).
[in]	tol	is a tolerance for inexact objective function computation.

Definition at line 163 of file ROL_Objective.hpp.

References ROL_UNUSED.

Referenced by ROL::TypeP::TrustRegionAlgorithm< Real >::dprox(), ROL::TypeP::InexactNewtonAlgorithm< Real >::initialize(), ROL::TypeP::iPianoAlgorithm< Real >::initialize(), ROL::TypeP::ProxGradientAlgorithm< Real >::initialize(), ROL::TypeP::QuasiNewtonAlgorithm< Real >::initialize(), ROL::TypeP::SpectralGradientAlgorithm< Real >::initialize(), ROL::TypeP::TrustRegionAlgorithm< Real >::initialize(), ROL::TypeP::Algorithm< Real >::pgstep(), and ROL::TypeP::iPianoAlgorithm< Real >::run().

proxJacVec()

template<typename Real>

virtual void ROL::Objective< Real >::proxJacVec ( Vector< Real > & Jv, const Vector< Real > & v, const Vector< Real > & x, Real t, Real & tol )

virtual

Apply the Jacobian of the proximity operator.

This function applies the Jacobian of the proximity operator.

Parameters

[out]	Jv	is the Jacobian of the proximity operator at \(x\) applied to \(v\) (primal optimization vector).
[in]	v	is the direction vector (primal optimization vector).
[in]	x	is the input to the proximity operator (primal optimization vector).
[in]	t	is the proximity operator parameter (positive scalar).
[in]	tol	is a tolerance for inexact objective function computation.

checkGradient() [1/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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 204 of file ROL_Objective.hpp.

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

Referenced by checkGradient(), checkGradient(), and main().

checkGradient() [2/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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)

References ROL_NUM_CHECKDERIV_STEPS.

checkGradient() [3/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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 264 of file ROL_Objective.hpp.

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

checkGradient() [4/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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)

checkHessVec() [1/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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 326 of file ROL_Objective.hpp.

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

Referenced by checkHessVec(), checkHessVec(), and main().

checkHessVec() [2/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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)

References ROL_NUM_CHECKDERIV_STEPS.

checkHessVec() [3/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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 387 of file ROL_Objective.hpp.

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

checkHessVec() [4/4]

template<typename Real>

virtual std::vector< std::vector< Real > > 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)

checkHessSym() [1/2]

template<typename Real>

virtual std::vector< Real > 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 442 of file ROL_Objective.hpp.

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

Referenced by checkHessSym().

checkHessSym() [2/2]

template<typename Real>

virtual std::vector< Real > 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.

checkProxJacVec()

template<typename Real>

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

virtual

Finite-difference proximity operator Jacobian-applied-to-vector check.

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

\[ \left\| \frac{\mathrm{prox}_{t f}(x+tv) - \mathrm{prox}_{t f}(x)}{t} - J_{t f}(x+tv)v\right\|_{\mathcal{X}}, \]

if the approximation is first order. Note that in some cases the proximity operator is semismooth, which motivates the evaluation of \(J_{t f}\) at \(x+tv\).

Parameters

[in]	x	is an optimization vector.
[in]	v	is a direction vector.
[in]	t	is the proximity operator parameter.
[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.

References ROL_NUM_CHECKDERIV_STEPS.

getParameter()

template<typename Real>

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

inlineprotected

Definition at line 504 of file ROL_Objective.hpp.

References param_.

Referenced by ROL::RegressionError< Real >::checkSize(), ROL::RegressionError< Real >::gradient(), ROL::Reduced_Objective_SimOpt< Real >::solve_adjoint_equation(), ROL::Reduced_Objective_SimOpt< Real >::solve_state_equation(), and ROL::RegressionError< Real >::value().

setParameter()

template<typename Real>

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

inlinevirtual

Definition at line 509 of file ROL_Objective.hpp.

References param_.

Referenced by ROL::CompositeObjective< Real >::setParameter(), ROL::LinearCombinationObjective< Real >::setParameter(), ROL::MoreauYosidaPenalty< Real >::setParameter(), ROL::PH_bPOEObjective< Real >::setParameter(), ROL::PH_DeviationObjective< Real >::setParameter(), ROL::PH_ErrorObjective< Real >::setParameter(), ROL::PH_Objective< Real >::setParameter(), ROL::PH_ProbObjective< Real >::setParameter(), ROL::PH_RegretObjective< Real >::setParameter(), ROL::PH_RiskObjective< Real >::setParameter(), ROL::Reduced_Objective_SimOpt< Real >::setParameter(), ROL::RiskLessObjective< Real >::setParameter(), ROL::ROL::AffineTransformObjective< Real >::setParameter(), ROL::ROL::NonlinearLeastSquaresObjective< Real >::setParameter(), ROL::ScaledObjective< Real >::setParameter(), and ROL::SlacklessObjective< Real >::setParameter().

Member Data Documentation

prim_

template<typename Real>

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

private

Definition at line 47 of file ROL_Objective.hpp.

Referenced by Objective().

dual_

template<typename Real>

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

private

Definition at line 47 of file ROL_Objective.hpp.

Referenced by Objective().

basis_

template<typename Real>

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

private

Definition at line 47 of file ROL_Objective.hpp.

Referenced by Objective().

param_

template<typename Real>

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

private

Definition at line 501 of file ROL_Objective.hpp.

Referenced by getParameter(), and setParameter().

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

• ROL_Objective.hpp