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. More...

	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. More...

	AugmentedLagrangian ()
	Null constructor. More...

virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function. More...

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

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

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

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

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::Objective< Real >
virtual	~Objective ()

	Objective ()

virtual void	update (const Vector< Real > &x, UpdateType type, 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)
	Compute the proximity operator. 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 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::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

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(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

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.

Definition at line 125 of file ROL_AugmentedLagrangian.hpp.

References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

template<class Real>

ROL::AugmentedLagrangian< Real >::AugmentedLagrangian ( )

inline

Null constructor.

This constructor is only used for inheritance and does not create a valid AugmentedLagrangian object. Do not use.

Definition at line 150 of file ROL_AugmentedLagrangian.hpp.

Member Function Documentation

template<class Real>

virtual void ROL::AugmentedLagrangian< Real >::update	(	const Vector< Real > &	x,
		bool	flag = `true`,
		int	iter = `-1`
	)

inlinevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters

[in]	x	is the new iterate.
[in]	flag	is true if the iterate has changed.
[in]	iter	is the outer algorithm iterations count.

Reimplemented from ROL::Objective< Real >.

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 156 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::obj_, and ROL::AugmentedLagrangian< Real >::pen_.

Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().

template<class Real>

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

inline

Definition at line 163 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::fscale_, and ROL::AugmentedLagrangian< Real >::pen_.

Referenced by ROL::AugmentedLagrangianStep< Real >::initialize().

template<class Real>

virtual Real ROL::AugmentedLagrangian< 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 >.

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 168 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::fval_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::nfval_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

template<class Real>

virtual void ROL::AugmentedLagrangian< 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 >.

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 184 of file ROL_AugmentedLagrangian.hpp.

Referenced by ROL::AugmentedLagrangianStep< Real >::computeGradient().

template<class Real>

virtual void ROL::AugmentedLagrangian< 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.