Provides the interface to evaluate the weighted/shifted l1 objective function. More...

#include <ROL_l1Objective.hpp>

Inheritance diagram for ROL::l1Objective< Real >:

Classes
struct	ProjSymBnd

Public Member Functions
	l1Objective (const Ptr< Vector< Real >> &weights)

	l1Objective (const Ptr< Vector< Real >> &weights, const Ptr< Vector< Real >> &shift)

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

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

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

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

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

const Ptr< Vector< Real > >	shift_

Ptr< Vector< Real > >	tmp_

ROL::l1Objective::ProjSymBnd	psb_

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::l1Objective< Real >

Provides the interface to evaluate the weighted/shifted l1 objective function.

Definition at line 26 of file ROL_l1Objective.hpp.

Constructor & Destructor Documentation

template<typename Real >

ROL::l1Objective< Real >::l1Objective ( const Ptr< Vector< Real >> & weights )

inline

Definition at line 37 of file ROL_l1Objective.hpp.

References ROL::l1Objective< Real >::shift_, and ROL::l1Objective< Real >::tmp_.

template<typename Real >

ROL::l1Objective< Real >::l1Objective	(	const Ptr< Vector< Real >> &	weights,
		const Ptr< Vector< Real >> &	shift
	)

inline

Definition at line 43 of file ROL_l1Objective.hpp.

References ROL::l1Objective< Real >::shift_, and ROL::l1Objective< Real >::tmp_.

Member Function Documentation

template<typename Real >

Real ROL::l1Objective< Real >::value	(	const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

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 48 of file ROL_l1Objective.hpp.

References ROL::l1Objective< Real >::shift_, ROL::l1Objective< Real >::tmp_, and ROL::l1Objective< Real >::weights_.

template<typename Real >

void ROL::l1Objective< Real >::gradient	(	Vector< Real > &	g,
		const Vector< Real > &	x,
		Real &	tol
	)

inlinevirtual

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 55 of file ROL_l1Objective.hpp.

References ROL::Vector< Real >::applyBinary(), ROL::Vector< Real >::applyUnary(), ROL::Vector< Real >::axpy(), ROL::Vector< Real >::set(), ROL::l1Objective< Real >::shift_, and ROL::l1Objective< Real >::weights_.

Referenced by ROL::l1Objective< Real >::dirDeriv().

template<typename Real >

Real ROL::l1Objective< Real >::dirDeriv	(	const Vector< Real > &	x,
		const Vector< Real > &	d,
		Real &	tol
	)

inlinevirtual

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.

Reimplemented from ROL::Objective< Real >.

Definition at line 62 of file ROL_l1Objective.hpp.

References ROL::l1Objective< Real >::gradient(), and ROL::l1Objective< Real >::tmp_.

template<typename Real >

void ROL::l1Objective< 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.