Provides an interface to run equality constrained optimization algorithms using the Composite-Step Trust-Region Sequential Quadratic Programming (SQP) method. More...

#include <ROL_TypeE_CompositeStepAlgorithm.hpp>

Inheritance diagram for ROL::TypeE::CompositeStepAlgorithm< Real >:

Public Member Functions
	CompositeStepAlgorithm (ParameterList &list)

virtual void	run (Vector< Real > &x, const Vector< Real > &g, Objective< Real > &obj, Constraint< Real > &econ, Vector< Real > &emul, const Vector< Real > &eres, std::ostream &outStream=std::cout) override
	Run algorithm on equality constrained problems (Type-E). This general interface supports the use of dual optimization vector spaces, where the user does not define the dual() method.

virtual void	writeHeader (std::ostream &os) const override
	Print iterate header.

virtual void	writeName (std::ostream &os) const override
	Print step name.

virtual void	writeOutput (std::ostream &os, const bool print_header=false) const override
	Print iterate status.

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

	Algorithm ()
	Constructor, given a step and a status test.

void	setStatusTest (const Ptr< StatusTest< Real > > &status, bool combineStatus=false)

virtual void	run (Problem< Real > &problem, std::ostream &outStream=std::cout)
	Run algorithm on equality constrained problems (Type-E). This is the primary Type-E interface.

virtual void	run (Vector< Real > &x, Objective< Real > &obj, Constraint< Real > &econ, Vector< Real > &emul, std::ostream &outStream=std::cout)
	Run algorithm on equality constrained problems (Type-E). This is the primary Type-E interface.

virtual void	run (Vector< Real > &x, Objective< Real > &obj, Constraint< Real > &econ, Vector< Real > &emul, Constraint< Real > &linear_econ, Vector< Real > &linear_emul, std::ostream &outStream=std::cout)
	Run algorithm on equality constrained problems with explicit linear equality constraints (Type-E). This is the primary Type-E with explicit linear equality constraints interface.

virtual void	run (Vector< Real > &x, const Vector< Real > &g, Objective< Real > &obj, Constraint< Real > &econ, Vector< Real > &emul, const Vector< Real > &eres, Constraint< Real > &linear_econ, Vector< Real > &linear_emul, const Vector< Real > &linear_eres, std::ostream &outStream=std::cout)
	Run algorithm on equality constrained problems with explicit linear equality constraints (Type-E). This general interface supports the use of dual optimization vector spaces, where the user does not define the dual() method.

virtual void	writeExitStatus (std::ostream &os) const

Ptr< const AlgorithmState< Real > >	getState () const

void	reset ()

Private Member Functions
void	initialize (Vector< Real > &x, const Vector< Real > &g, Vector< Real > &l, const Vector< Real > &c, Objective< Real > &obj, Constraint< Real > &con, std::ostream &outStream=std::cout)
	Initialize algorithm by computing a few quantities.

void	computeTrial (Vector< Real > &s, const Vector< Real > &x, const Vector< Real > &l, Objective< Real > &obj, Constraint< Real > &con, std::ostream &os)
	Compute trial step.

void	updateRadius (Vector< Real > &x, Vector< Real > &l, const Vector< Real > &s, Objective< Real > &obj, Constraint< Real > &con, std::ostream &os)
	Update trust-region radius, take step, etc.

void	computeLagrangeMultiplier (Vector< Real > &l, const Vector< Real > &x, const Vector< Real > &gf, Constraint< Real > &con, std::ostream &os)
	Compute Lagrange multipliers by solving the least-squares problem minimizing the gradient of the Lagrangian, via the augmented system formulation.

void	computeQuasinormalStep (Vector< Real > &n, const Vector< Real > &c, const Vector< Real > &x, Real delta, Constraint< Real > &con, std::ostream &os)
	Compute quasi-normal step by minimizing the norm of the linearized constraint.

void	solveTangentialSubproblem (Vector< Real > &t, Vector< Real > &tCP, Vector< Real > &Wg, const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &n, const Vector< Real > &l, Real delta, Objective< Real > &obj, Constraint< Real > &con, std::ostream &os)
	Solve tangential subproblem.

void	accept (Vector< Real > &s, Vector< Real > &n, Vector< Real > &t, Real f_new, Vector< Real > &c_new, Vector< Real > &gf_new, Vector< Real > &l_new, Vector< Real > &g_new, const Vector< Real > &x, const Vector< Real > &l, Real f, const Vector< Real > &gf, const Vector< Real > &c, const Vector< Real > &g, Vector< Real > &tCP, Vector< Real > &Wg, Objective< Real > &obj, Constraint< Real > &con, std::ostream &os)
	Check acceptance of subproblem solutions, adjust merit function penalty parameter, ensure global convergence.

template<typename T >
int	sgn (T val) const

void	printInfoLS (const std::vector< Real > &res, std::ostream &os) const

Real	setTolOSS (const Real intol) const

Private Attributes
ParameterList	list_

ROL::Ptr< Vector< Real > >	xvec_

ROL::Ptr< Vector< Real > >	gvec_

ROL::Ptr< Vector< Real > >	cvec_

ROL::Ptr< Vector< Real > >	lvec_

int	flagCG_

int	flagAC_

int	iterCG_

int	maxiterCG_

int	maxiterOSS_

Real	tolCG_

Real	tolOSS_

bool	tolOSSfixed_

Real	lmhtol_

Real	qntol_

Real	pgtol_

Real	projtol_

Real	tangtol_

Real	tntmax_

Real	zeta_

Real	Delta_

Real	penalty_

Real	eta_

bool	useConHess_

Real	ared_

Real	pred_

Real	snorm_

Real	nnorm_

Real	tnorm_

bool	infoQN_

bool	infoLM_

bool	infoTS_

bool	infoAC_

bool	infoLS_

bool	infoALL_

int	totalIterCG_

int	totalProj_

int	totalNegCurv_

int	totalRef_

int	totalCallLS_

int	totalIterLS_

int	verbosity_

bool	printHeader_

Additional Inherited Members
Protected Member Functions inherited from ROL::TypeE::Algorithm< Real >
void	initialize (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &mul, const Vector< Real > &c)

Protected Attributes inherited from ROL::TypeE::Algorithm< Real >
const Ptr< CombinedStatusTest< Real > >	status_

const Ptr< AlgorithmState< Real > >	state_

Detailed Description

template<typename Real>
class ROL::TypeE::CompositeStepAlgorithm< Real >

Provides an interface to run equality constrained optimization algorithms using the Composite-Step Trust-Region Sequential Quadratic Programming (SQP) method.

Definition at line 24 of file ROL_TypeE_CompositeStepAlgorithm.hpp.

Constructor & Destructor Documentation

◆ CompositeStepAlgorithm()

template<typename Real >

ROL::TypeE::CompositeStepAlgorithm< Real >::CompositeStepAlgorithm ( ParameterList & list )

Definition at line 17 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

Member Function Documentation

◆ initialize()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::initialize	(	Vector< Real > &	x,
		const Vector< Real > &	g,
		Vector< Real > &	l,
		const Vector< Real > &	c,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		std::ostream &	outStream = `std::cout`
	)

private

Initialize algorithm by computing a few quantities.

Definition at line 987 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Vector< Real >::clone(), ROL::Objective< Real >::gradient(), ROL::Initial, ROL::TypeE::Algorithm< Real >::initialize(), ROL::Constraint< Real >::update(), ROL::Objective< Real >::update(), ROL::Objective< Real >::value(), and ROL::Constraint< Real >::value().

◆ computeTrial()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::computeTrial	(	Vector< Real > &	s,
		const Vector< Real > &	x,
		const Vector< Real > &	l,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Compute trial step.

Definition at line 82 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Objective< Real >::gradient(), ROL::Objective< Real >::value(), and ROL::Constraint< Real >::value().

◆ updateRadius()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::updateRadius	(	Vector< Real > &	x,
		Vector< Real > &	l,
		const Vector< Real > &	s,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Update trust-region radius, take step, etc.

Definition at line 916 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Accept, ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Objective< Real >::gradient(), ROL::Vector< Real >::plus(), ROL::Revert, ROL::Constraint< Real >::update(), ROL::Objective< Real >::update(), ROL::Objective< Real >::value(), ROL::Constraint< Real >::value(), and zero.

◆ computeLagrangeMultiplier()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::computeLagrangeMultiplier	(	Vector< Real > &	l,
		const Vector< Real > &	x,
		const Vector< Real > &	gf,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Compute Lagrange multipliers by solving the least-squares problem minimizing the gradient of the Lagrangian, via the augmented system formulation.

Parameters

[out]	l	is the updated Lagrange multiplier; a dual constraint-space vector
[in]	x	is the current iterate; an optimization-space vector
[in]	gf	is the gradient of the objective function; a dual optimization-space vector
[in]	con	is the equality constraint object

Definition at line 133 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Vector< Real >::plus(), and ROL::Constraint< Real >::solveAugmentedSystem().

◆ computeQuasinormalStep()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::computeQuasinormalStep	(	Vector< Real > &	n,
		const Vector< Real > &	c,
		const Vector< Real > &	x,
		Real	delta,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Compute quasi-normal step by minimizing the norm of the linearized constraint.

Compute an approximate solution of the problem

\[ \begin{array}{rl} \min_{n} & \|c'(x_k)n + c(x_k)\|^2_{\mathcal{X}} \\ \mbox{subject to} & \|n\|_{\mathcal{X}} \le \delta \end{array} \]

The approximate solution is computed using Powell's dogleg method. The dogleg path is computed using the Cauchy point and a full Newton step. The path's intersection with the trust-region constraint gives the quasi-normal step.

Parameters

[out]	n	is the quasi-normal step; an optimization-space vector
[in]	c	is the value of equality constraints; a constraint-space vector
[in]	x	is the current iterate; an optimization-space vector
[in]	delta	is the trust-region radius for the quasi-normal step
[in]	con	is the equality constraint object

Definition at line 183 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Constraint< Real >::applyJacobian(), ROL::Vector< Real >::axpy(), ROL::Vector< Real >::dual(), ROL::Vector< Real >::scale(), ROL::Vector< Real >::set(), ROL::Constraint< Real >::solveAugmentedSystem(), and zero.

◆ solveTangentialSubproblem()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::solveTangentialSubproblem	(	Vector< Real > &	t,
		Vector< Real > &	tCP,
		Vector< Real > &	Wg,
		const Vector< Real > &	x,
		const Vector< Real > &	g,
		const Vector< Real > &	n,
		const Vector< Real > &	l,
		Real	delta,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Solve tangential subproblem.

   @param[out]      t     is the solution of the tangential subproblem; an optimization-space vector
   @param[out]      tCP   is the Cauchy point for the tangential subproblem; an optimization-space vector
   @param[out]      Wg    is the dual of the projected gradient of the Lagrangian; an optimization-space vector
   @param[in]       x     is the current iterate; an optimization-space vector
   @param[in]       g     is the gradient of the Lagrangian; a dual optimization-space vector
   @param[in]       n     is the quasi-normal step; an optimization-space vector
   @param[in]       l     is the Lagrange multiplier; a dual constraint-space vector
   @param[in]       delta is the trust-region radius for the tangential subproblem
   @param[in]       obj   is the objective function
   @param[in]       con   is the equality constraint object

Definition at line 286 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Constraint< Real >::applyAdjointHessian(), ROL::Constraint< Real >::applyJacobian(), ROL::Vector< Real >::dot(), ROL::Vector< Real >::dual(), ROL::Objective< Real >::hessVec(), ROL::Vector< Real >::norm(), ROL::Vector< Real >::plus(), ROL::Vector< Real >::set(), ROL::Constraint< Real >::solveAugmentedSystem(), zero, and ROL::Vector< Real >::zero().

◆ accept()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::accept	(	Vector< Real > &	s,
		Vector< Real > &	n,
		Vector< Real > &	t,
		Real	f_new,
		Vector< Real > &	c_new,
		Vector< Real > &	gf_new,
		Vector< Real > &	l_new,
		Vector< Real > &	g_new,
		const Vector< Real > &	x,
		const Vector< Real > &	l,
		Real	f,
		const Vector< Real > &	gf,
		const Vector< Real > &	c,
		const Vector< Real > &	g,
		Vector< Real > &	tCP,
		Vector< Real > &	Wg,
		Objective< Real > &	obj,
		Constraint< Real > &	con,
		std::ostream &	os
	)

private

Check acceptance of subproblem solutions, adjust merit function penalty parameter, ensure global convergence.

Definition at line 620 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Vector< Real >::apply(), ROL::Constraint< Real >::applyAdjointHessian(), ROL::Constraint< Real >::applyAdjointJacobian(), ROL::Constraint< Real >::applyJacobian(), ROL::Vector< Real >::dot(), ROL::Objective< Real >::gradient(), ROL::Objective< Real >::hessVec(), ROL::Vector< Real >::norm(), ROL::Vector< Real >::plus(), ROL::Vector< Real >::set(), ROL::Constraint< Real >::solveAugmentedSystem(), ROL::Trial, ROL::Constraint< Real >::update(), ROL::Objective< Real >::update(), ROL::Objective< Real >::value(), ROL::Constraint< Real >::value(), and zero.

◆ sgn()

template<typename Real >

template<typename T >

int ROL::TypeE::CompositeStepAlgorithm< Real >::sgn ( T val ) const

private

Definition at line 1159 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

◆ printInfoLS()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::printInfoLS	(	const std::vector< Real > &	res,
		std::ostream &	os
	)		const

private

Definition at line 1165 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

◆ setTolOSS()

template<typename Real >

Real ROL::TypeE::CompositeStepAlgorithm< Real >::setTolOSS ( const Real intol ) const

private

Definition at line 1181 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

◆ run()

template<typename Real >

void ROL::TypeE::CompositeStepAlgorithm< Real >::run	(	Vector< Real > &	x,
		const Vector< Real > &	g,
		Objective< Real > &	obj,
		Constraint< Real > &	econ,
		Vector< Real > &	emul,
		const Vector< Real > &	eres,
		std::ostream &	outStream = `std::cout`
	)

overridevirtual

Run algorithm on equality constrained problems (Type-E). This general interface supports the use of dual optimization vector spaces, where the user does not define the dual() method.

Implements ROL::TypeE::Algorithm< Real >.

Definition at line 1030 of file ROL_TypeE_CompositeStepAlgorithm_Def.hpp.

References ROL::Vector< Real >::clone(), and ROL::TypeE::Algorithm< Real >::writeExitStatus().

Referenced by main().