Provides the interface to evaluate the elastic augmented Lagrangian. More...

#include <ROL_ElasticObjective.hpp>

Inheritance diagram for ROL::ElasticObjective< Real >:

Public Member Functions
	ElasticObjective (const Ptr< Objective< Real >> &obj, const Ptr< Constraint< Real >> &con, const Real penaltyParameter, const Real sigma, const Vector< Real > &dualOptVec, const Vector< Real > &primConVec, const Vector< Real > &dualConVec, ParameterList &parlist)

	ElasticObjective (const Ptr< Objective< Real >> &obj, const Ptr< Constraint< Real >> &con, const Real penaltyParameter, const Real sigma, const Vector< Real > &dualOptVec, const Vector< Real > &primConVec, const Vector< Real > &dualConVec, const bool scaleLagrangian, const int HessianApprox)

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

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	setScaling (const Real fscale=1.0, const Real cscale=1.0)

Real	getObjectiveValue (const Vector< Real > &x, Real &tol)

const Ptr< const Vector< Real > >	getObjectiveGradient (const Vector< Real > &x, Real &tol)

const Ptr< const Vector< Real > >	getConstraintVec (const Vector< Real > &x, Real &tol)

int	getNumberConstraintEvaluations (void) const

int	getNumberFunctionEvaluations (void) const

int	getNumberGradientEvaluations (void) const

void	reset (const Vector< Real > &multiplier, Real penaltyParameter, Real sigma)

const Ptr < AugmentedLagrangianObjective < Real > >	getAugmentedLagrangian (void) const

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

	Objective ()

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)

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

Private Attributes
Ptr < AugmentedLagrangianObjective < Real > >	alobj_

Ptr< Vector< Real > >	e_

Ptr< Vector< Real > >	tmp_

Real	sigma_

Real	cscale_

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::ElasticObjective< Real >

Provides the interface to evaluate the elastic augmented Lagrangian.

This class implements the elastic augmented Lagrangian functional for use with ROL::StablizedLCLAlgorithm. Given a function \(f:\mathcal{X}\to\mathbb{R}\) and an equality constraint \(c:\mathcal{X}\to\mathcal{C}\), the augmented Lagrangian functional is

\[ L_A(x,\lambda,\mu) = f(x) + \langle \lambda, c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} + \frac{\mu}{2} \langle \mathfrak{R}c(x),c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} + \sigma\langle \mathfrak{R} e, u-v\ranlge_{\mathcal{C}^*,\mathcal{C}} \]

where \(\lambda\in\mathcal{C}^*\) denotes the Lagrange multiplier estimate, \(\mu > 0\) and \(\sigma>0\) are penalty parameters, \(e\in\mathcal{C}\) is the constant one vector, and \(\mathfrak{R}\in\mathcal{L}(\mathcal{C},\mathcal{C}^*)\) is the Riesz operator on the constraint space.

This implementation permits the scaling of \(L_A\) by \(\mu^{-1}\) and also permits the Hessian approximation

\[ \nabla^2_x L_A(x,\lambda,\mu)v \approx \nabla^2 f(x) v + \mu c'(x)^*\mathfrak{R} c'(x)v. \]

Definition at line 49 of file ROL_ElasticObjective.hpp.

Constructor & Destructor Documentation

template<typename Real >

ROL::ElasticObjective< Real >::ElasticObjective	(	const Ptr< Objective< Real >> &	obj,
		const Ptr< Constraint< Real >> &	con,
		const Real	penaltyParameter,
		const Real	sigma,
		const Vector< Real > &	dualOptVec,
		const Vector< Real > &	primConVec,
		const Vector< Real > &	dualConVec,
		ParameterList &	parlist
	)

Definition at line 17 of file ROL_ElasticObjective_Def.hpp.

References ROL::ElasticObjective< Real >::alobj_, ROL::ElasticObjective< Real >::e_, and ROL::ElasticObjective< Real >::tmp_.

template<typename Real >

ROL::ElasticObjective< Real >::ElasticObjective	(	const Ptr< Objective< Real >> &	obj,
		const Ptr< Constraint< Real >> &	con,
		const Real	penaltyParameter,
		const Real	sigma,
		const Vector< Real > &	dualOptVec,
		const Vector< Real > &	primConVec,
		const Vector< Real > &	dualConVec,
		const bool	scaleLagrangian,
		const int	HessianApprox
	)

Definition at line 32 of file ROL_ElasticObjective_Def.hpp.

References ROL::ElasticObjective< Real >::alobj_, ROL::ElasticObjective< Real >::e_, and ROL::ElasticObjective< Real >::tmp_.

Member Function Documentation

template<typename Real >

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

overridevirtual

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 from ROL::Objective< Real >.

Definition at line 48 of file ROL_ElasticObjective_Def.hpp.

template<typename Real >

Real ROL::ElasticObjective< 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 60 of file ROL_ElasticObjective_Def.hpp.

template<typename Real >

void ROL::ElasticObjective< 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 71 of file ROL_ElasticObjective_Def.hpp.

template<typename Real >

void ROL::ElasticObjective< 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.