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

#include <ROL_AugmentedLagrangianObjective.hpp>

Inheritance diagram for ROL::AugmentedLagrangianObjective< Real >:

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

	AugmentedLagrangianObjective (const Ptr< Objective< Real >> &obj, const Ptr< Constraint< Real >> &con, const Real penaltyParameter, 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)
	Update objective function. More...

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

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...

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

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, const Real penaltyParameter)

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
const Ptr< Objective< Real > >	obj_

const Ptr< Constraint< Real > >	con_

Real	penaltyParameter_

Ptr< Vector< Real > >	multiplier_

Ptr< Vector< Real > >	dualOptVector_

Ptr< Vector< Real > >	dualConVector_

Ptr< Vector< Real > >	primConVector_

Ptr< ScalarController< Real, int > >	fval_

Ptr< VectorController< Real, int > >	gradient_

Ptr< VectorController< Real, int > >	conValue_

Real	fscale_

Real	cscale_

int	nfval_

int	ngval_

int	ncval_

bool	scaleLagrangian_

int	HessianApprox_

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

Detailed Description

template<class Real>
class ROL::AugmentedLagrangianObjective< Real >

Provides the interface to evaluate the augmented Lagrangian.

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

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

where \(\lambda\in\mathcal{C}^*\) denotes the Lagrange multiplier estimate, \(\mu > 0\) is the penalty parameter 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 88 of file ROL_AugmentedLagrangianObjective.hpp.

Constructor & Destructor Documentation

template<class Real>

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

inline

Definition at line 121 of file ROL_AugmentedLagrangianObjective.hpp.

template<class Real>

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

inline

Definition at line 145 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::Vector< Real >::clone(), ROL::AugmentedLagrangianObjective< Real >::conValue_, ROL::AugmentedLagrangianObjective< Real >::dualConVector_, ROL::AugmentedLagrangianObjective< Real >::dualOptVector_, ROL::AugmentedLagrangianObjective< Real >::fval_, ROL::AugmentedLagrangianObjective< Real >::gradient_, ROL::AugmentedLagrangianObjective< Real >::multiplier_, and ROL::AugmentedLagrangianObjective< Real >::primConVector_.

Member Function Documentation

template<class Real>

void ROL::AugmentedLagrangianObjective< 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 from ROL::Objective< Real >.

Definition at line 167 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::AugmentedLagrangianObjective< Real >::con_, ROL::AugmentedLagrangianObjective< Real >::conValue_, ROL::AugmentedLagrangianObjective< Real >::fval_, ROL::AugmentedLagrangianObjective< Real >::gradient_, and ROL::AugmentedLagrangianObjective< Real >::obj_.

Referenced by ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::initialize(), and ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::initialize().

template<class Real>

void ROL::AugmentedLagrangianObjective< Real >::setScaling	(	const Real	fscale = `1.0`,
		const Real	cscale = `1.0`
	)

inline

Definition at line 175 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::AugmentedLagrangianObjective< Real >::cscale_, and ROL::AugmentedLagrangianObjective< Real >::fscale_.

Referenced by ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::initialize(), and ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::initialize().

template<class Real>

Real ROL::AugmentedLagrangianObjective< 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 180 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::AugmentedLagrangianObjective< Real >::cscale_, ROL::AugmentedLagrangianObjective< Real >::fscale_, ROL::AugmentedLagrangianObjective< Real >::getConstraintVec(), ROL::AugmentedLagrangianObjective< Real >::getObjectiveValue(), ROL::AugmentedLagrangianObjective< Real >::multiplier_, ROL::AugmentedLagrangianObjective< Real >::penaltyParameter_, ROL::AugmentedLagrangianObjective< Real >::primConVector_, and ROL::AugmentedLagrangianObjective< Real >::scaleLagrangian_.

template<class Real>

void ROL::AugmentedLagrangianObjective< 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 196 of file ROL_AugmentedLagrangianObjective.hpp.

Referenced by ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::initialize(), ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::initialize(), ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::run(), and ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::run().

template<class Real>

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

inlinevirtual

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.