Provides the interface to compute augmented Lagrangian steps. More...

#include <ROL_AugmentedLagrangianStep.hpp>

Inheritance diagram for ROL::AugmentedLagrangianStep< Real >:

Public Member Functions
	~AugmentedLagrangianStep ()

	AugmentedLagrangianStep (ROL::ParameterList &parlist)

void	initialize (Vector< Real > &x, const Vector< Real > &g, Vector< Real > &l, const Vector< Real > &c, Objective< Real > &obj, Constraint< Real > &con, AlgorithmState< Real > &algo_state)
	Initialize step with equality constraint. More...

void	initialize (Vector< Real > &x, const Vector< Real > &g, Vector< Real > &l, const Vector< Real > &c, Objective< Real > &obj, Constraint< Real > &con, BoundConstraint< Real > &bnd, AlgorithmState< Real > &algo_state)
	Initialize step with equality and bound constraints. More...

void	compute (Vector< Real > &s, const Vector< Real > &x, const Vector< Real > &l, Objective< Real > &obj, Constraint< Real > &con, AlgorithmState< Real > &algo_state)
	Compute step (equality constraint). More...

void	compute (Vector< Real > &s, const Vector< Real > &x, const Vector< Real > &l, Objective< Real > &obj, Constraint< Real > &con, BoundConstraint< Real > &bnd, AlgorithmState< Real > &algo_state)
	Compute step (equality and bound constraints). More...

void	update (Vector< Real > &x, Vector< Real > &l, const Vector< Real > &s, Objective< Real > &obj, Constraint< Real > &con, AlgorithmState< Real > &algo_state)
	Update step, if successful (equality constraint). More...

void	update (Vector< Real > &x, Vector< Real > &l, const Vector< Real > &s, Objective< Real > &obj, Constraint< Real > &con, BoundConstraint< Real > &bnd, AlgorithmState< Real > &algo_state)
	Update step, if successful (equality and bound constraints). More...

std::string	printHeader (void) const
	Print iterate header. More...

std::string	printName (void) const
	Print step name. More...

std::string	print (AlgorithmState< Real > &algo_state, bool pHeader=false) const
	Print iterate status. More...

void	compute (Vector< Real > &s, const Vector< Real > &x, Objective< Real > &obj, BoundConstraint< Real > &con, AlgorithmState< Real > &algo_state)
	Compute step for bound constraints; here only to satisfy the interface requirements, does nothing, needs refactoring. More...

void	update (Vector< Real > &x, const Vector< Real > &s, Objective< Real > &obj, BoundConstraint< Real > &con, AlgorithmState< Real > &algo_state)
	Update step, for bound constraints; here only to satisfy the interface requirements, does nothing, needs refactoring. More...

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

	Step (void)

virtual void	initialize (Vector< Real > &x, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con, AlgorithmState< Real > &algo_state)
	Initialize step with bound constraint. More...

virtual void	initialize (Vector< Real > &x, const Vector< Real > &s, const Vector< Real > &g, Objective< Real > &obj, BoundConstraint< Real > &con, AlgorithmState< Real > &algo_state)
	Initialize step with bound constraint. More...

void	initialize (OptimizationProblem< Real > &opt, AlgorithmState< Real > &algo_state)

void	compute (Vector< Real > &s, OptimizationProblem< Real > &opt, AlgorithmState< Real > &algo_state)

void	update (OptimizationProblem< Real > &opt, const Vector< Real > &s, AlgorithmState< Real > &algo_state)

const ROL::Ptr< const StepState< Real > >	getStepState (void) const
	Get state for step object. More...

void	reset (const Real searchSize=1.0)
	Get state for step object. More...

Private Member Functions
Real	computeGradient (Vector< Real > &g, const Vector< Real > &x, const Real mu, Objective< Real > &obj, BoundConstraint< Real > &bnd)

Private Attributes
ROL::Ptr< Algorithm< Real > >	algo_

ROL::Ptr< Vector< Real > >	x_

ROL::Ptr< BoundConstraint< Real > >	bnd_

ROL::ParameterList	parlist_

bool	useDefaultInitPen_

bool	scaleLagrangian_

Real	minPenaltyReciprocal_

Real	minPenaltyLowerBound_

Real	penaltyUpdate_

Real	maxPenaltyParam_

Real	optIncreaseExponent_

Real	optDecreaseExponent_

Real	optToleranceInitial_

Real	optTolerance_

Real	feasIncreaseExponent_

Real	feasDecreaseExponent_

Real	feasToleranceInitial_

Real	feasTolerance_

bool	print_

int	maxit_

int	subproblemIter_

std::string	subStep_

Real	outerOptTolerance_

Real	outerFeasTolerance_

Real	outerStepTolerance_

bool	useDefaultScaling_

Real	fscale_

Real	cscale_

int	verbosity_

Additional Inherited Members
Protected Member Functions inherited from ROL::Step< Real >
ROL::Ptr< StepState< Real > >	getState (void)

Detailed Description

template<class Real>
class ROL::AugmentedLagrangianStep< Real >

Provides the interface to compute augmented Lagrangian steps.

The Augmented Lagrangian algorithm is used to solve Type-EB problems. This algorithm solves the scaled problem

\[ \min_{x} w_J J(x) \quad\text{subject to}\quad w_c c(x) = 0,\quad \ell \le x \le u \]

for some positive consants \(w_J,\, w_c\). These constants are either input by the user or automatically estimated. To solve this scaled problem, the Augmented Lagrangian algorithm minimizes the so-called Augmented Lagrangian functional

\[ L(x,\lambda,r) := w_J J(x) + w_c \langle \lambda, c(x)\rangle_{X^*,X} + \frac{w_c^2 r}{2} \|c(x)\|_X^2 \]

subject to the bound constraints \(\ell \le x \le u\). The multiplier estimate \(\lambda\) is updated as

\[ \lambda \leftarrow \lambda + r w_c c(x). \]

The penalty parameter \(r>0\) is also updated based on the progress of the algorithm. The initial penalty parameter is either input by the user or automatically computed.

User Input Parameters: bool Step -> Augmented Lagrangian -> Use Default initial Penalty Parameter Use automatically determined initial penalty parameter. Default: true

Real Step -> Augmented Lagrangian -> Initial Penalty Parameter Initial penalty parameter. Default: 10

Real Step -> Augmented Lagrangian -> Use Scaled Augmented Lagrangian Use Augmented Lagrangian scaled by the reciprocal of the penalty parameter. Default: false

Real Step -> Augmented Lagrangian -> Penalty Parameter Reciprocal Lower Bound Minimum penalty parameter reciprocal for tolerance updates. Default: 0.1

Real Step -> Augmented Lagrangian -> Penalty Parameter Growth Factor Rate of growth for penalty parameter. Default: 10

Real Step -> Augmented Lagrangian -> Maximum Penalty Parameter Maximum penalty parameter size. Default: 1e8

Real Step -> Augmented Lagrangian -> Optimality Tolerance Update Exponent Rate at which to update optimality tolerance. Default: 1

Real Step -> Augmented Lagrangian -> Optimality Tolerance Decrease Exponent Rate at which to decrease optimality tolerance. Default: 1

Real Step -> Augmented Lagrangian -> Initial Optimality Tolerance Initial tolerance for optimality. Default: 1

Real Step -> Augmented Lagrangian -> Feasibility Tolerance Update Exponent Rate at which to update feasibility tolerance. Default: 0.1

Real Step -> Augmented Lagrangian -> Feasibility Tolerance Decrease Exponent Rate at which to decrease feasibility tolerance. Default: 0.9

Real Step -> Augmented Lagrangian -> Initial Feasibility Tolerance Initial tolerance for equality constraint feasibility. Default: 1

bool Step -> Augmented Lagrangian -> Print Intermediate Optimization History Print iteration history for subproblem solve. Default: false

int Step -> Augmented Lagrangian -> Subproblem Iteration Limit Subproblem iteration limit. Default: 1000

string Step -> Augmented Lagrangian -> Subproblem Step Type Subproblem (bound constrained) solver type. Default: Trust Region

bool Step -> Augmented Lagrangian -> Use Default Problem Scaling Use automatic constraint and objective scaling. Default: true

Real Step -> Augmented Lagrangian -> Objective Scaling Positive scaling constant for objective. Default: 1

Real Step -> Augmented Lagrangian -> Constraint Scaling Positive scaling constant for constraint. Default: 1

int General -> Print Verbosity Print additional information to screen for debugging purposes. Default: 0

Definition at line 144 of file ROL_AugmentedLagrangianStep.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::AugmentedLagrangianStep< Real >::~AugmentedLagrangianStep ( )

inline

Definition at line 213 of file ROL_AugmentedLagrangianStep.hpp.

template<class Real >

ROL::AugmentedLagrangianStep< Real >::AugmentedLagrangianStep ( ROL::ParameterList & parlist )

inline

Definition at line 215 of file ROL_AugmentedLagrangianStep.hpp.

Member Function Documentation

template<class Real >

Real ROL::AugmentedLagrangianStep< Real >::computeGradient	(	Vector< Real > &	g,
		const Vector< Real > &	x,
		const Real	mu,
		Objective< Real > &	obj,
		BoundConstraint< Real > &	bnd
	)

inlineprivate

Definition at line 183 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::gradient(), ROL::BoundConstraint< Real >::isActivated(), ROL::Vector< Real >::norm(), ROL::BoundConstraint< Real >::project(), ROL::Vector< Real >::scale(), ROL::AugmentedLagrangianStep< Real >::scaleLagrangian_, and ROL::AugmentedLagrangianStep< Real >::x_.

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

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::initialize	(	Vector< Real > &	x,
		const Vector< Real > &	g,
		Vector< Real > &	l,
		const Vector< Real > &	c,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Initialize step with equality constraint.

Reimplemented from ROL::Step< Real >.

Definition at line 257 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::bnd_.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::initialize	(	Vector< Real > &	x,
		const Vector< Real > &	g,
		Vector< Real > &	l,
		const Vector< Real > &	c,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		BoundConstraint< Real > &	bnd,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Initialize step with equality and bound constraints.

Reimplemented from ROL::Step< Real >.

Definition at line 267 of file ROL_AugmentedLagrangianStep.hpp.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::compute	(	Vector< Real > &	s,
		const Vector< Real > &	x,
		const Vector< Real > &	l,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Compute step (equality constraint).

Reimplemented from ROL::Step< Real >.

Definition at line 342 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::bnd_.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::compute	(	Vector< Real > &	s,
		const Vector< Real > &	x,
		const Vector< Real > &	l,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		BoundConstraint< Real > &	bnd,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Compute step (equality and bound constraints).

Reimplemented from ROL::Step< Real >.

Definition at line 350 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::algo_, ROL::Vector< Real >::axpy(), ROL::BoundConstraint< Real >::isActivated(), ROL::AugmentedLagrangianStep< Real >::optTolerance_, ROL::AugmentedLagrangianStep< Real >::parlist_, ROL::AugmentedLagrangianStep< Real >::print_, ROL::Vector< Real >::set(), ROL::AugmentedLagrangianStep< Real >::subproblemIter_, ROL::AugmentedLagrangianStep< Real >::subStep_, and ROL::AugmentedLagrangianStep< Real >::x_.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::update	(	Vector< Real > &	x,
		Vector< Real > &	l,
		const Vector< Real > &	s,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Update step, if successful (equality constraint).

Reimplemented from ROL::Step< Real >.

Definition at line 372 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::bnd_.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::update	(	Vector< Real > &	x,
		Vector< Real > &	l,
		const Vector< Real > &	s,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		BoundConstraint< Real > &	bnd,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Update step, if successful (equality and bound constraints).

Reimplemented from ROL::Step< Real >.

Definition at line 380 of file ROL_AugmentedLagrangianStep.hpp.

template<class Real >

std::string ROL::AugmentedLagrangianStep< Real >::printHeader ( void ) const

inlinevirtual

Print iterate header.

Reimplemented from ROL::Step< Real >.

Definition at line 434 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::verbosity_.

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

template<class Real >

std::string ROL::AugmentedLagrangianStep< Real >::printName ( void ) const

inlinevirtual

Print step name.

Reimplemented from ROL::Step< Real >.

Definition at line 473 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AugmentedLagrangianStep< Real >::subStep_.

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

template<class Real >

std::string ROL::AugmentedLagrangianStep< Real >::print	(	AlgorithmState< Real > &	algo_state,
		bool	pHeader = `false`
	)		const

inlinevirtual

Print iterate status.

Reimplemented from ROL::Step< Real >.

Definition at line 483 of file ROL_AugmentedLagrangianStep.hpp.

References ROL::AlgorithmState< Real >::cnorm, ROL::AugmentedLagrangianStep< Real >::feasTolerance_, ROL::AlgorithmState< Real >::gnorm, ROL::AlgorithmState< Real >::iter, ROL::AlgorithmState< Real >::ncval, ROL::AlgorithmState< Real >::nfval, ROL::AlgorithmState< Real >::ngrad, ROL::AugmentedLagrangianStep< Real >::optTolerance_, ROL::AugmentedLagrangianStep< Real >::outerFeasTolerance_, ROL::AugmentedLagrangianStep< Real >::outerOptTolerance_, ROL::AugmentedLagrangianStep< Real >::printHeader(), ROL::AugmentedLagrangianStep< Real >::printName(), ROL::AlgorithmState< Real >::snorm, ROL::AugmentedLagrangianStep< Real >::subproblemIter_, and ROL::AlgorithmState< Real >::value.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::compute	(	Vector< Real > &	s,
		const Vector< Real > &	x,
		Objective< Real > &	obj,
		BoundConstraint< Real > &	con,
		AlgorithmState< Real > &	algo_state
	)

inlinevirtual

Compute step for bound constraints; here only to satisfy the interface requirements, does nothing, needs refactoring.

Reimplemented from ROL::Step< Real >.

Definition at line 529 of file ROL_AugmentedLagrangianStep.hpp.

template<class Real >

void ROL::AugmentedLagrangianStep< Real >::update	(	Vector< Real > &	x,
		const Vector< Real > &	s,
		Objective< Real > &	obj,
		BoundConstraint< Real > &	con,
		AlgorithmState< Real > &	algo_state
	)