Provides the interface to evaluate the quadratic quasi-Newton objective. More...

#include <ROL_PQNObjective.hpp>

Inheritance diagram for ROL::PQNObjective< Real >:

Public Member Functions
	PQNObjective (const Ptr< Secant< Real >> &secant, const Vector< Real > &x, const Vector< Real > &g)

Real	value (const Vector< Real > &x, Real &tol) override
	Compute value. More...

void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol) override
	Compute gradient. More...

void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
	Apply Hessian approximation to vector. More...

void	setAnchor (const Vector< Real > &x, const Vector< Real > &g)

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

	Objective ()

virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update objective function. More...

virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function. More...

virtual Real	dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol)
	Compute directional derivative. More...

virtual void	invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply inverse Hessian approximation to vector. More...

virtual void	precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply preconditioner to vector. More...

virtual void	prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
	Compute the proximity operator. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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

Private Attributes
const Ptr< Secant< Real > >	secant_

const Ptr< Vector< Real > >	x_

const Ptr< Vector< Real > >	g_

const Ptr< Vector< Real > >	pwa_

const Ptr< Vector< Real > >	dwa_

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

Detailed Description

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

Provides the interface to evaluate the quadratic quasi-Newton objective.

This class implements the PQN quasi-Newton objective for use with ROL::TypeB::QuasiNewtonAlgorithm. Given a function \(f:\mathcal{X}\to\mathbb{R}\) and a Hessian approximation \(B_k:\mathcal{X}\to\mathcal{X}^*\), the functional is

\[ q_k(x) = \frac{1}{2}\langle B_k (x-x_k),(x-x_k)\rangle_{\mathcal{X}^*,\mathcal{X}} + \langle f'(x_k), (x-x_k)\rangle_{\mathcal{X}^*,\mathcal{X}}. \]

Definition at line 36 of file ROL_PQNObjective.hpp.

Constructor & Destructor Documentation

template<typename Real >

ROL::PQNObjective< Real >::PQNObjective	(	const Ptr< Secant< Real >> &	secant,
		const Vector< Real > &	x,
		const Vector< Real > &	g
	)

Definition at line 17 of file ROL_PQNObjective_Def.hpp.

References ROL::PQNObjective< Real >::setAnchor().

Member Function Documentation

template<typename Real >

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

overridevirtual

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.

Implements ROL::Objective< Real >.

Definition at line 25 of file ROL_PQNObjective_Def.hpp.

template<typename Real >

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

overridevirtual

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 from ROL::Objective< Real >.

Definition at line 35 of file ROL_PQNObjective_Def.hpp.

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

template<typename Real >

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

overridevirtual

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 from ROL::Objective< Real >.

Definition at line 43 of file ROL_PQNObjective_Def.hpp.

template<typename Real >

void ROL::PQNObjective< Real >::setAnchor	(	const Vector< Real > &	x,
		const Vector< Real > &	g
	)

Definition at line 48 of file ROL_PQNObjective_Def.hpp.

Referenced by ROL::PQNObjective< Real >::PQNObjective().

Member Data Documentation

template<typename Real >

const Ptr<Secant<Real> > ROL::PQNObjective< Real >::secant_

private

Definition at line 38 of file ROL_PQNObjective.hpp.

template<typename Real >

const Ptr<Vector<Real> > ROL::PQNObjective< Real >::x_

private

Definition at line 39 of file ROL_PQNObjective.hpp.

template<typename Real >

const Ptr<Vector<Real> > ROL::PQNObjective< Real >::g_

private

Definition at line 39 of file ROL_PQNObjective.hpp.

template<typename Real >

const Ptr<Vector<Real> > ROL::PQNObjective< Real >::pwa_

private

Definition at line 39 of file ROL_PQNObjective.hpp.

template<typename Real >

const Ptr<Vector<Real> > ROL::PQNObjective< Real >::dwa_

private

Definition at line 39 of file ROL_PQNObjective.hpp.

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

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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