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.
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.
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).
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).
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).
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).
std::string	printHeader (void) const
	Print iterate header.
std::string	printName (void) const
	Print step name.
std::string	print (AlgorithmState< Real > &algo_state, bool pHeader=false) const
	Print iterate status.
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.
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.
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.
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.
const ROL::Ptr< const StepState< Real > >	getStepState (void) const
	Get state for step object.
void	reset (const Real searchSize=1.0)
	Get state for step object.

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< StatusTest< Real > >	status_
ROL::Ptr< Step< Real > >	step_
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 126 of file ROL_AugmentedLagrangianStep.hpp.

Constructor & Destructor Documentation

◆ ~AugmentedLagrangianStep()

template<class Real>

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

inline

Definition at line 197 of file ROL_AugmentedLagrangianStep.hpp.

◆ AugmentedLagrangianStep()

template<class Real>

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

inline

Member Function Documentation

◆ computeGradient()

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 167 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::ROL_EPSILON(), ROL::Vector< Real >::scale(), scaleLagrangian_, and x_.

Referenced by initialize(), and update().

◆ initialize() [1/2]

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 241 of file ROL_AugmentedLagrangianStep.hpp.

References bnd_, and initialize().

Referenced by initialize().

◆ initialize() [2/2]

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 251 of file ROL_AugmentedLagrangianStep.hpp.

◆ compute() [1/3]

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 325 of file ROL_AugmentedLagrangianStep.hpp.

References bnd_, and compute().

Referenced by compute().

◆ compute() [2/3]

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 333 of file ROL_AugmentedLagrangianStep.hpp.

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

◆ update() [1/3]

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 394 of file ROL_AugmentedLagrangianStep.hpp.

References bnd_, and update().

Referenced by update().

◆ update() [2/3]

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 402 of file ROL_AugmentedLagrangianStep.hpp.

◆ printHeader()

template<class Real>

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

inlinevirtual

Print iterate header.

Reimplemented from ROL::Step< Real >.

Definition at line 458 of file ROL_AugmentedLagrangianStep.hpp.

References verbosity_.

Referenced by print().

◆ printName()

template<class Real>

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

inlinevirtual

Print step name.

Reimplemented from ROL::Step< Real >.

Definition at line 497 of file ROL_AugmentedLagrangianStep.hpp.

References subStep_.

Referenced by print().

◆ 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 507 of file ROL_AugmentedLagrangianStep.hpp.

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

◆ compute() [3/3]

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 553 of file ROL_AugmentedLagrangianStep.hpp.

◆ update() [3/3]

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 )