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

#include <ROL_AugmentedLagrangianObjective.hpp>

Inheritance diagram for AugmentedLagrangianObjective:

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)

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

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

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

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

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, 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 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 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

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

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

Constructor & Destructor Documentation

◆ AugmentedLagrangianObjective() [1/2]

AugmentedLagrangianObjective::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 120 of file ROL_AugmentedLagrangianObjective.hpp.

◆ AugmentedLagrangianObjective() [2/2]

AugmentedLagrangianObjective::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 )