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

#include <ROL_AugmentedLagrangian.hpp>

Inheritance diagram for ROL::AugmentedLagrangian< Real >:

Public Member Functions
	AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, ROL::ParameterList &parlist)
	Constructor.
	AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, const bool scaleLagrangian, const int HessianApprox)
	Constructor.
	AugmentedLagrangian ()
	Null constructor.
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
void	setScaling (const Real fscale, const Real cscale=1.0)
virtual Real	value (const Vector< Real > &x, Real &tol)
virtual void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
virtual void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
virtual Real	getObjectiveValue (const Vector< Real > &x)
const Ptr< const Vector< Real > >	getObjectiveGradient (const Vector< Real > &x)
virtual void	getConstraintVec (Vector< Real > &c, const Vector< Real > &x)
virtual int	getNumberConstraintEvaluations (void) const
virtual int	getNumberFunctionEvaluations (void) const
virtual int	getNumberGradientEvaluations (void) const
virtual void	reset (const Vector< Real > &multiplier, const Real penaltyParameter)
Public Member Functions inherited from ROL::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 void	prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
	Compute the proximity operator.
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.
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 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.
virtual void	setParameter (const std::vector< Real > &param)

Private Attributes
const ROL::Ptr< Objective< Real > >	obj_
ROL::Ptr< QuadraticPenalty< Real > >	pen_
Real	penaltyParameter_
ROL::Ptr< Vector< Real > >	dualOptVector_
Real	fval_
ROL::Ptr< Vector< Real > >	gradient_
Real	fscale_
int	nfval_
int	ngval_
bool	scaleLagrangian_
bool	isValueComputed_
bool	isGradientComputed_

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

Detailed Description

template<class Real>
class ROL::AugmentedLagrangian< Real >

Provides the interface to evaluate the augmented Lagrangian.

This class implements the augmented Lagrangian functional for use with ROL::AugmentedLagrangianStep. 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 52 of file ROL_AugmentedLagrangian.hpp.

Constructor & Destructor Documentation

◆ AugmentedLagrangian() [1/3]

template<class Real>

ROL::AugmentedLagrangian< Real >::AugmentedLagrangian	(	const ROL::Ptr< Objective< Real > > &	obj,
		const ROL::Ptr< Constraint< Real > > &	con,
		const Vector< Real > &	multiplier,
		const Real	penaltyParameter,
		const Vector< Real > &	optVec,
		const Vector< Real > &	conVec,
		ROL::ParameterList &	parlist )

inline

Constructor.

This creates a valid AugmentedLagrangian object.

Parameters

[in]	obj	is an objective function.
[in]	con	is an equality constraint.
[in]	mulitplier	is a Lagrange multiplier vector.
[in]	penaltyParameter	is the penalty parameter.
[in]	optVec	is an optimization space vector.
[in]	conVec	is a constraint space vector.
[in]	parlist	is a parameter list.

Definition at line 92 of file ROL_AugmentedLagrangian.hpp.

References ROL::Vector< Real >::dual(), dualOptVector_, fscale_, fval_, gradient_, isGradientComputed_, isValueComputed_, nfval_, ngval_, obj_, ROL::ROL::Objective< Real >::Objective(), pen_, penaltyParameter_, and scaleLagrangian_.

◆ AugmentedLagrangian() [2/3]

template<class Real>

ROL::AugmentedLagrangian< Real >::AugmentedLagrangian	(	const ROL::Ptr< Objective< Real > > &	obj,
		const ROL::Ptr< Constraint< Real > > &	con,
		const Vector< Real > &	multiplier,
		const Real	penaltyParameter,
		const Vector< Real > &	optVec,
		const Vector< Real > &	conVec,
		const bool	scaleLagrangian,
		const int	HessianApprox )

inline

Constructor.

This creates a valid AugmentedLagrangian object.

Parameters

[in]	obj	is an objective function.
[in]	con	is an equality constraint.
[in]	mulitplier	is a Lagrange multiplier vector.
[in]	penaltyParameter	is the penalty parameter.
[in]	optVec	is an optimization space vector.
[in]	conVec	is a constraint space vector.
[in]	parlist	is a parameter list.