A class implementing the BFGS optimizer based on conjugate gradient direction method of M. More...

#include <BFGS_Powell.h>

Inheritance diagram for BFGS_Powell:

Public Member Functions
	BFGS_Powell (void(f_pointer)(Matrix_real, void , double , Matrix_real &), void meta_data_in)
	Constructor of the class. More...

double	Start_Optimization (Matrix_real &x, long maximal_iterations_in=5001)
	Call this method to start the optimization. More...

	~BFGS_Powell ()
	Destructor of the class. More...

Protected Member Functions
void	BFGS_iteration (Matrix_real &x, Matrix_real &g, Matrix_real &x0_search, Matrix_real &g0_search, double &norm_Z)
	Method implementing the BFGS update of the matrix Z. More...

void	get_f_ang_gradient (Matrix_real &x, double &f, Matrix_real &g)
	Call this method to obtain the cost function and its gradient at a gives position given by x. More...

void	get_Maximal_Line_Search_Step (Matrix_real &search_direction, double &maximal_step, double &search_direction__grad_overlap)
	Call this method to obtain the maximal step size during the line search. More...

void	get_search_direction (Matrix_real &g, Matrix_real &search_direction, double &search_direction__grad_overlap)
	Method to get the search direction in the next line search. More...

void	Initialize_Zmtx ()
	Initialize the matrix Z to identity. More...

void	line_search (Matrix_real &x, Matrix_real &g, Matrix_real &search_direction, Matrix_real &x0_search, Matrix_real &g0_search, double &maximal_step, double &d__dot__g, double &f)
	Call to perform inexact line search terminated with Wolfe 1st and 2nd conditions. More...

void	Optimize (Matrix_real &x, double &f)
	Call this method to start the optimization process. More...

Protected Attributes
void(*	costfnc__and__gradient )(Matrix_real x, void params, double f, Matrix_real &g)
	function pointer to evaluate the cost function and its gradient vector More...

void(*	export_fnc )(double, Matrix_real &, void *)
	function pointer to evaluate the cost function and its gradient vector More...

long	function_call_count
	number of function calls during the optimization process More...

long	maximal_iterations
	maximal count of iterations during the optimization More...

void *	meta_data
	additional data needed to evaluate the cost function More...

double	num_precision
	numerical precision used in the calculations More...

enum solver_status	status
	status of the solver More...

int	variable_num
	number of independent variables in the problem More...

Matrix_real	Z_T__dot__g

Matrix_real	Zmtx

Detailed Description

A class implementing the BFGS optimizer based on conjugate gradient direction method of M.

J. D. Powell: A tolerant algorithm for linearly constrained optimization calculations, Mathematical Programming volume 45, pages 547â566 (1989)

Definition at line 26 of file BFGS_Powell.h.

Constructor & Destructor Documentation

◆ BFGS_Powell()

BFGS_Powell::BFGS_Powell	(	void()(Matrix_real, void , double *, Matrix_real &)	f_pointer,
		void *	meta_data_in
	)

Constructor of the class.

Parameters

f_pointer	A function pointer (x, meta_data, f, grad) to evaluate the cost function and its gradients. The cost function and the gradient vector are returned via reference by the two last arguments.
meta_data	void pointer to additional meta data needed to evaluate the cost function.

Returns: An instance of the class

Definition at line 32 of file BFGS_Powell.cpp.

◆ ~BFGS_Powell()

BFGS_Powell::~BFGS_Powell ( )

Destructor of the class.

Definition at line 444 of file BFGS_Powell.cpp.

Member Function Documentation

◆ BFGS_iteration()

void BFGS_Powell::BFGS_iteration	(	Matrix_real &	x,
		Matrix_real &	g,
		Matrix_real &	x0,
		Matrix_real &	g0,
		double &	norm_Z
	)

protected

Method implementing the BFGS update of the matrix Z.

See M.J.D. POWELL: UPDATING CONJUGATE DIRECTIONS BY THE BFGS FORMULA, Mathematical Programming 38 (1987) 29-46 for details.

Parameters

x	The current coordinates.
g	The gradient at the current coordinates.
x0_search	The starting point used at the previous line search
g0_search	The gradient at x0_search
norm_Z	The column-wise norm of the matrix Z is updated (and returned) via this argument.

See M.J.D. POWELL: UPDATING CONJUGATE DIRECTIONS BY THE BFGS FORMULA, Mathematical Programming 38 (1987) 29-46 for details.

Parameters

x	The current coordinates.
g	The current coordinates gradient.
x0_search	The starting point used at the previous line search
g0_search	The gradient at x0_search
d__dot__g	The overlap of the search direction and the gradient calculated in get_search_direction

Definition at line 202 of file BFGS_Powell.cpp.

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◆ get_f_ang_gradient()

void Grad_Descend::get_f_ang_gradient	(	Matrix_real &	x,
		double &	f,
		Matrix_real &	g
	)

protectedinherited

Call this method to obtain the cost function and its gradient at a gives position given by x.

Parameters

x	The array of the current coordinates
f	The value of the cost function is returned via this argument.
g	The gradient of the cost function at x.

Definition at line 443 of file common/grad_descend.cpp.

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◆ get_Maximal_Line_Search_Step()

void Grad_Descend::get_Maximal_Line_Search_Step	(	Matrix_real &	search_direction,
		double &	maximal_step,
		double &	search_direction__grad_overlap
	)

protectedinherited

Call this method to obtain the maximal step size during the line search.

providing at least 2*PI periodicity, unless the search direction component in a specific direction is to small.

Parameters

search_direction	The search direction.
maximal_step	The maximal allowed step in the search direction returned via this argument.
search_direction__grad_overlap	The overlap of the gradient with the search direction to test downhill.

Providing at least 2*PI periodicity, unless the search direction component in a specific direction is to small.

Parameters

search_direction	The search direction.
maximal_step	The maximal allowed step in the search direction returned via this argument.
search_direction__grad_overlap	The overlap of the gradient with the search direction to test downhill.

Definition at line 401 of file common/grad_descend.cpp.

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◆ get_search_direction()

void BFGS_Powell::get_search_direction	(	Matrix_real &	g,
		Matrix_real &	search_direction,
		double &	search_direction__grad_overlap
	)

protectedvirtual

Method to get the search direction in the next line search.

Parameters

g	The gradient at the current coordinates.
search_direction	The search direction is returned via this argument (calculated with g and with Zmtx)
search_direction__grad_overlap	The overlap of the gradient with the search direction to test downhill.

Reimplemented from Grad_Descend.

Definition at line 396 of file BFGS_Powell.cpp.

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◆ Initialize_Zmtx()

void BFGS_Powell::Initialize_Zmtx ( )

protected

Initialize the matrix Z to identity.

See the definition of matrix Z at Eq (1.8) in M. J. D. Powell: A tolerant algorithm for linearly constrained optimization calculations, Mathematical Programming volume 45, pages 547â566 (1989)

Definition at line 41 of file BFGS_Powell.cpp.

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◆ line_search()

void Grad_Descend::line_search	(	Matrix_real &	x,
		Matrix_real &	g,
		Matrix_real &	search_direction,
		Matrix_real &	x0_search,
		Matrix_real &	g0_search,
		double &	maximal_step,
		double &	d__dot__g0,
		double &	f
	)

protectedinherited

Call to perform inexact line search terminated with Wolfe 1st and 2nd conditions.

Parameters

x	The guess for the starting point. The coordinated of the optimized cost function are returned via x.
g	The gradient at x. The updated gradient is returned via this argument.
search_direction	The search direction.
x0_search	Stores the starting point. (automatically updated with the starting x during the execution)
g0_search	Stores the starting gradient. (automatically updated with the starting x during the execution)
maximal_step	The maximal allowed step in the search direction
d__dot__g	The overlap of the gradient with the search direction to test downhill.
f	The value of the minimized cost function is returned via this argument

Definition at line 127 of file common/grad_descend.cpp.

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◆ Optimize()

void BFGS_Powell::Optimize	(	Matrix_real &	x,
		double &	f
	)

protectedvirtual

Call this method to start the optimization process.

Parameters

x	The guess for the starting point. The coordinated of the optimized cost function are returned via x.
f	The value of the minimized cost function

Reimplemented from Grad_Descend.

Definition at line 70 of file BFGS_Powell.cpp.

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◆ Start_Optimization()

double Grad_Descend::Start_Optimization	(	Matrix_real &	x,
		long	maximal_iterations_in = `5001`
	)

inherited

Call this method to start the optimization.

Parameters

x	The initial solution guess.
maximal_iterations_in	The maximal number of function+gradient evaluations. Reaching this threshold the solver returns with the current solution.

Definition at line 83 of file common/grad_descend.cpp.

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Member Data Documentation

◆ costfncandgradient

void(* Grad_Descend::costfnc__and__gradient) (Matrix_real x, void *params, double *f, Matrix_real &g)

protectedinherited

function pointer to evaluate the cost function and its gradient vector

Definition at line 50 of file grad_descend.h.

◆ export_fnc

void(* Grad_Descend::export_fnc) (double, Matrix_real &, void *)

protectedinherited

function pointer to evaluate the cost function and its gradient vector

Definition at line 53 of file grad_descend.h.

◆ function_call_count

long Grad_Descend::function_call_count

protectedinherited

number of function calls during the optimization process

Definition at line 44 of file grad_descend.h.

◆ maximal_iterations

long Grad_Descend::maximal_iterations

protectedinherited

maximal count of iterations during the optimization

Definition at line 41 of file grad_descend.h.

◆ meta_data

void* Grad_Descend::meta_data

protectedinherited

additional data needed to evaluate the cost function

Definition at line 56 of file grad_descend.h.

◆ num_precision

double Grad_Descend::num_precision

protectedinherited

numerical precision used in the calculations

Definition at line 47 of file grad_descend.h.

◆ status

enum solver_status Grad_Descend::status

protectedinherited

status of the solver

Definition at line 59 of file grad_descend.h.

◆ variable_num

int Grad_Descend::variable_num

protectedinherited

number of independent variables in the problem

Definition at line 38 of file grad_descend.h.

◆ Z_Tdotg

Matrix_real BFGS_Powell::Z_T__dot__g

protected

Definition at line 37 of file BFGS_Powell.h.

◆ Zmtx

Matrix_real BFGS_Powell::Zmtx

protected

Definition at line 34 of file BFGS_Powell.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BFGS_Powell()

◆ ~BFGS_Powell()

Member Function Documentation

◆ BFGS_iteration()

◆ get_f_ang_gradient()

◆ get_Maximal_Line_Search_Step()

◆ get_search_direction()

◆ Initialize_Zmtx()

◆ line_search()

◆ Optimize()

◆ Start_Optimization()

Member Data Documentation

◆ costfnc__and__gradient

◆ export_fnc

◆ function_call_count

◆ maximal_iterations

◆ meta_data

◆ num_precision

◆ status

◆ variable_num

◆ Z_T__dot__g

◆ Zmtx

◆ costfncandgradient

◆ Z_Tdotg