Class implementing a modified BFGS optimization scheme. More...

#include <BFGSNonLinearSolver.h>

Inheritance diagram for dftfe::BFGSNonLinearSolver:

Public Member Functions
	BFGSNonLinearSolver (const bool usePreconditioner, const bool useRFOStep, const unsigned int maxNumberIterations, const unsigned int debugLevel, const MPI_Comm &mpi_comm_parent, const double trustRadius_maximum=0.5, const double trustRadius_initial=0.02, const double trustRadius_minimum=1.0e-4, const bool isCurvatureOnlyLineSearchStoppingCondition=false)
	Constructor.

	~BFGSNonLinearSolver ()
	Destructor.

nonLinearSolver::ReturnValueType	solve (nonlinearSolverProblem &problem, const std::string checkpointFileName="", const bool restart=false)
	Solve non-linear problem using a modified BFGS method.

void	save (const std::string &checkpointFileName)
	Create checkpoint file for current state of the BFGS solver.

Public Member Functions inherited from dftfe::nonLinearSolver
virtual	~nonLinearSolver ()=0
	Destructor.

Private Member Functions
void	initializeHessian (nonlinearSolverProblem &problem)
	initialize hessian, either preconditioner or identity matrix.

void	updateHessian ()
	Update Hessian according to damped BFGS rule: Procedure 18.2 of Nocedal and Wright.

void	scaleHessian ()
	Scale hessian according to eqn 6.20 of Nocedal and Wright.

void	checkWolfe ()
	Check if the step satifies the Strong Wolfe conditons.

void	computeRFOStep ()
	Compute step using the Rational Function Method.

void	computeNewtonStep ()
	Compute the Quasi-Newton Step.

void	computeStep ()
	Compute the final update step using the trust radius and whether or not the previous step was accepted.

void	computeTrustRadius (nonlinearSolverProblem &problem)
	Estimate the trust radius for the next step based on the previous step and check for trust radius max/min conditons and reset BFGS if needed.

bool	updateSolution (const std::vector< double > &step, nonlinearSolverProblem &problem)
	Update solution x -> x + step.

void	load (const std::string &checkpointFileName)
	Load BFGS solver state from checkpoint file.

Private Attributes
std::vector< double >	d_gradient

std::vector< double >	d_value

std::vector< double >	d_gradientNew

std::vector< double >	d_valueNew

std::vector< double >	d_deltaX

std::vector< double >	d_deltaXNew

std::vector< double >	d_updateVector

unsigned int	d_numberUnknowns

unsigned int	d_iter
	storage for current bfgs iteration count

std::vector< double >	d_Srfo

std::vector< double >	d_hessian
	storage for the hessian in current bfgs step.

double	d_normDeltaXnew
	storage for inf norm of the update step.

double	d_trustRadiusInitial
	storage for trust region parameters.

double	d_trustRadiusMax

double	d_trustRadiusMin

double	d_trustRadius

bool	d_stepAccepted
	boolean parameter for step accepteance and Wolfe conditions.

bool	d_wolfeCurvature

bool	d_wolfeSufficientDec

bool	d_wolfeSatisfied

bool	d_hessianScaled

bool	d_isCurvatureOnlyLineSearchStoppingCondition

int	d_isReset

bool	d_useSingleAtomSolutionsInitialGuess

const bool	d_useRFOStep

const bool	d_usePreconditioner

MPI_Comm	mpi_communicator

dealii::ConditionalOStream	pcout

Additional Inherited Members
Public Types inherited from dftfe::nonLinearSolver
enum	ReturnValueType { SUCCESS = 0 , FAILURE , LINESEARCH_FAILED , MAX_ITER_REACHED , RESTART }

Protected Member Functions inherited from dftfe::nonLinearSolver
	nonLinearSolver (const unsigned int debugLevel, const unsigned int maxNumberIterations, const double tolerance=0)
	Constructor.

double	getTolerance () const
	Get tolerance.

unsigned int	getMaximumNumberIterations () const
	Get maximum number of iterations.

unsigned int	getDebugLevel () const
	Get debug level.

Protected Attributes inherited from dftfe::nonLinearSolver
const unsigned int	d_debugLevel
	controls the verbosity of the printing

const unsigned int	d_maxNumberIterations
	maximum number of nonlinear solve iterations

const double	d_tolerance
	nonlinear solve stopping tolerance

Detailed Description

Class implementing a modified BFGS optimization scheme.

Author: Nikhil Kodali

Constructor & Destructor Documentation

◆ BFGSNonLinearSolver()

dftfe::BFGSNonLinearSolver::BFGSNonLinearSolver	(	const bool	usePreconditioner,
		const bool	useRFOStep,
		const unsigned int	maxNumberIterations,
		const unsigned int	debugLevel,
		const MPI_Comm &	mpi_comm_parent,
		const double	trustRadius_maximum = 0.5,
		const double	trustRadius_initial = 0.02,
		const double	trustRadius_minimum = 1.0e-4,
		const bool	isCurvatureOnlyLineSearchStoppingCondition = false )

Constructor.

Parameters

usePreconditioner	Boolean parameter specifying whether or not to use the preconditioner.
useRFOStep	Boolean parameter specifying whether or not the RFO step is used.
maxNumberIterations	Maximum number of iterations.
debugLevel	Debug output level: 0 - no debug output 1 - limited debug output 2 - all debug output.
mpi_comm_parent	The mpi communicator used.
trustRadius_maximum	Maximum trust region radius.
trustRadius_initial	Initial trust region radius.
trustRadius_minimum	mimimum trust region radius (will reset BFGS).

◆ ~BFGSNonLinearSolver()

dftfe::BFGSNonLinearSolver::~BFGSNonLinearSolver ( )

Destructor.

Member Function Documentation

◆ checkWolfe()

void dftfe::BFGSNonLinearSolver::checkWolfe ( )

private

Check if the step satifies the Strong Wolfe conditons.

◆ computeNewtonStep()

void dftfe::BFGSNonLinearSolver::computeNewtonStep ( )

private

Compute the Quasi-Newton Step.

◆ computeRFOStep()

void dftfe::BFGSNonLinearSolver::computeRFOStep ( )

private

Compute step using the Rational Function Method.

◆ computeStep()

void dftfe::BFGSNonLinearSolver::computeStep ( )

private

Compute the final update step using the trust radius and whether or not the previous step was accepted.

◆ computeTrustRadius()

void dftfe::BFGSNonLinearSolver::computeTrustRadius ( nonlinearSolverProblem & problem )

private

Estimate the trust radius for the next step based on the previous step and check for trust radius max/min conditons and reset BFGS if needed.

◆ initializeHessian()

void dftfe::BFGSNonLinearSolver::initializeHessian ( nonlinearSolverProblem & problem )

private

initialize hessian, either preconditioner or identity matrix.

◆ load()

void dftfe::BFGSNonLinearSolver::load ( const std::string & checkpointFileName )

private

Load BFGS solver state from checkpoint file.

◆ save()

void dftfe::BFGSNonLinearSolver::save ( const std::string & checkpointFileName )

virtual

Create checkpoint file for current state of the BFGS solver.

Implements dftfe::nonLinearSolver.

◆ scaleHessian()

void dftfe::BFGSNonLinearSolver::scaleHessian ( )

private

Scale hessian according to eqn 6.20 of Nocedal and Wright.

◆ solve()

nonLinearSolver::ReturnValueType dftfe::BFGSNonLinearSolver::solve	(	nonlinearSolverProblem &	problem,
		const std::string	checkpointFileName = "",
		const bool	restart = false )

virtual

Solve non-linear problem using a modified BFGS method.

Parameters

problem[in]	nonlinearSolverProblem object.
checkpointFileName[in]	if string is non-empty, creates checkpoint file named checkpointFileName for every nonlinear iteration. If restart is set to true, checkpointFileName must match the name of the checkpoint file. Empty string will throw an error.
restart[in]	boolean specifying whether this is a restart solve using the checkpoint file specified by checkpointFileName.

Returns: Return value indicating success or failure.

Implements dftfe::nonLinearSolver.

◆ updateHessian()

void dftfe::BFGSNonLinearSolver::updateHessian ( )

private

Update Hessian according to damped BFGS rule: Procedure 18.2 of Nocedal and Wright.

◆ updateSolution()

bool dftfe::BFGSNonLinearSolver::updateSolution	(	const std::vector< double > &	step,
		nonlinearSolverProblem &	problem )

private

Update solution x -> x + step.

Parameters

step	update step vector.
problem	nonlinearSolverProblem object.

Returns: bool true if valid update and false if increment bound exceeded

Member Data Documentation

◆ d_deltaX

std::vector<double> dftfe::BFGSNonLinearSolver::d_deltaX

private

storage for the step taken in last BFGS step, step computed in the corrent BFGS step and the update vector computed in the current bfgs step.

◆ d_deltaXNew

std::vector<double> dftfe::BFGSNonLinearSolver::d_deltaXNew

private

◆ d_gradient

std::vector<double> dftfe::BFGSNonLinearSolver::d_gradient

private

storage for the value and gradient of the nonlinear problem in the current bfgs step.

◆ d_gradientNew

std::vector<double> dftfe::BFGSNonLinearSolver::d_gradientNew

private

storage for the value and gradient of the nonlinear problem evaluated at the end of the current bfgs step.

◆ d_hessian

std::vector<double> dftfe::BFGSNonLinearSolver::d_hessian

private

storage for the hessian in current bfgs step.

◆ d_hessianScaled

bool dftfe::BFGSNonLinearSolver::d_hessianScaled

private

flag to check if hessian is scaled.

◆ d_isCurvatureOnlyLineSearchStoppingCondition

bool dftfe::BFGSNonLinearSolver::d_isCurvatureOnlyLineSearchStoppingCondition

private

◆ d_isReset

int dftfe::BFGSNonLinearSolver::d_isReset

private

Flag to store the reset state, 0 if step is accepted, 1 if reset occured and no steps are accepted, 2 if two resets occur without step being accepted (failure of BFGS).

◆ d_iter

unsigned int dftfe::BFGSNonLinearSolver::d_iter

private

storage for current bfgs iteration count

◆ d_normDeltaXnew

double dftfe::BFGSNonLinearSolver::d_normDeltaXnew

private

storage for inf norm of the update step.

◆ d_numberUnknowns

unsigned int dftfe::BFGSNonLinearSolver::d_numberUnknowns

private

storage for number of unknowns to be solved for in the nonlinear problem.

◆ d_Srfo

std::vector<double> dftfe::BFGSNonLinearSolver::d_Srfo

private

storage for the S matrix in RFO framework, initialized to starting. Hessian Guess

◆ d_stepAccepted

bool dftfe::BFGSNonLinearSolver::d_stepAccepted

private

boolean parameter for step accepteance and Wolfe conditions.

◆ d_trustRadius

double dftfe::BFGSNonLinearSolver::d_trustRadius

private

◆ d_trustRadiusInitial

double dftfe::BFGSNonLinearSolver::d_trustRadiusInitial

private

storage for trust region parameters.

◆ d_trustRadiusMax

double dftfe::BFGSNonLinearSolver::d_trustRadiusMax

private

◆ d_trustRadiusMin

double dftfe::BFGSNonLinearSolver::d_trustRadiusMin

private

◆ d_updateVector

std::vector<double> dftfe::BFGSNonLinearSolver::d_updateVector

private

◆ d_usePreconditioner

const bool dftfe::BFGSNonLinearSolver::d_usePreconditioner

private

◆ d_useRFOStep

const bool dftfe::BFGSNonLinearSolver::d_useRFOStep

private

◆ d_useSingleAtomSolutionsInitialGuess

bool dftfe::BFGSNonLinearSolver::d_useSingleAtomSolutionsInitialGuess

private

◆ d_value

std::vector<double> dftfe::BFGSNonLinearSolver::d_value

private

◆ d_valueNew

std::vector<double> dftfe::BFGSNonLinearSolver::d_valueNew

private

◆ d_wolfeCurvature

bool dftfe::BFGSNonLinearSolver::d_wolfeCurvature

private

◆ d_wolfeSatisfied

bool dftfe::BFGSNonLinearSolver::d_wolfeSatisfied

private

◆ d_wolfeSufficientDec

bool dftfe::BFGSNonLinearSolver::d_wolfeSufficientDec

private

◆ mpi_communicator

MPI_Comm dftfe::BFGSNonLinearSolver::mpi_communicator

private

◆ pcout

dealii::ConditionalOStream dftfe::BFGSNonLinearSolver::pcout

private

The documentation for this class was generated from the following file:

workspace/include/BFGSNonLinearSolver.h

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BFGSNonLinearSolver()

◆ ~BFGSNonLinearSolver()

Member Function Documentation

◆ checkWolfe()

◆ computeNewtonStep()

◆ computeRFOStep()

◆ computeStep()

◆ computeTrustRadius()

◆ initializeHessian()

◆ load()

◆ save()

◆ scaleHessian()

◆ solve()

◆ updateHessian()

◆ updateSolution()

Member Data Documentation

◆ d_deltaX

◆ d_deltaXNew

◆ d_gradient

◆ d_gradientNew

◆ d_hessian

◆ d_hessianScaled

◆ d_isCurvatureOnlyLineSearchStoppingCondition

◆ d_isReset

◆ d_iter

◆ d_normDeltaXnew

◆ d_numberUnknowns

◆ d_Srfo

◆ d_stepAccepted

◆ d_trustRadius

◆ d_trustRadiusInitial

◆ d_trustRadiusMax

◆ d_trustRadiusMin

◆ d_updateVector

◆ d_usePreconditioner

◆ d_useRFOStep

◆ d_useSingleAtomSolutionsInitialGuess

◆ d_value

◆ d_valueNew

◆ d_wolfeCurvature

◆ d_wolfeSatisfied

◆ d_wolfeSufficientDec

◆ mpi_communicator

◆ pcout