nonlin_optimize::bfgs Type Reference

Defines a Broyden–Fletcher–Goldfarb–Shanno (BFGS) solver for minimization of functions of multiple variables. More...

Inheritance diagram for nonlin_optimize::bfgs:

Public Member Functions
procedure, public	solve bfgs_solve
	Utilizes the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for finding a minimum value of the specified function.
Public Member Functions inherited from nonlin_optimize::line_search_optimizer
procedure, public	get_line_search lso_get_line_search
	Gets the line search module.
procedure, public	set_line_search lso_set_line_search
	Sets the line search module.
procedure, public	set_default_line_search lso_set_default
	Establishes a default line_search object for the line search module.
procedure, public	is_line_search_defined lso_is_line_search_defined
	Tests to see if a line search module is defined.
procedure, public	get_use_line_search lso_get_use_search
	Gets a value determining if a line-search should be employed.
procedure, public	set_use_line_search lso_set_use_search
	Sets a value determining if a line-search should be employed.
procedure, public	get_var_tolerance lso_get_var_tol
	Gets the convergence on change in variable tolerance.
procedure, public	set_var_tolerance lso_set_var_tol
	Sets the convergence on change in variable tolerance.
Public Member Functions inherited from nonlin_core::equation_optimizer
procedure, public	get_max_fcn_evals oe_get_max_eval
	Gets the maximum number of function evaluations allowed.
procedure, public	set_max_fcn_evals oe_set_max_eval
	Sets the maximum number of function evaluations allowed.
procedure, public	get_tolerance oe_get_tol
	Gets the tolerance on convergence.
procedure, public	set_tolerance oe_set_tol
	Sets the tolerance on convergence.
procedure, public	get_print_status oe_get_print_status
	Gets a logical value determining if iteration status should be printed.
procedure, public	set_print_status oe_set_print_status
	Sets a logical value determining if iteration status should be printed.

Additional Inherited Members
Public Attributes inherited from nonlin_optimize::line_search_optimizer
logical	m_uselinesearch = .true.
	Set to true if a line search should be used regardless of the status of m_lineSearch.
real(real64)	m_xtol = 1.0d-12
	The convergence criteria on change in variable.
Public Attributes inherited from nonlin_core::equation_optimizer
real(real64)	m_tol = 1.0d-12
	The error tolerance used to determine convergence.
logical	m_printstatus = .false.
	Set to true to print iteration status; else, false.

Detailed Description

Defines a Broyden–Fletcher–Goldfarb–Shanno (BFGS) solver for minimization of functions of multiple variables.

Definition at line 404 of file nonlin_optimize.f90.

Member Function/Subroutine Documentation

solve()

procedure, public nonlin_optimize::bfgs::solve

virtual

Utilizes the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for finding a minimum value of the specified function.

Syntax

subroutine solve(class(bfgs) this, class(fcnnvar_helper) fcn, real(real64) x(:), real(real64) fout, optional type(iteration_behavior) ib, optional class(errors) err)

Parameters

[in,out]	this	The bfgs_mead object.
[in]	fcn	The fcnnvar_helper object containing the equation to optimize.
[in,out]	x	On input, the initial guess at the optimal point. On output, the updated optimal point estimate.
[out]	fout	An optional output, that if provided, returns the value of the function at x.
[out]	ib	An optional output, that if provided, allows the caller to obtain iteration performance statistics.
[out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. NL_INVALID_OPERATION_ERROR: Occurs if no equations have been defined. NL_INVALID_INPUT_ERROR: Occurs if x is not appropriately sized for the problem as defined in fcn. NL_OUT_OF_MEMORY_ERROR: Occurs if there is insufficient memory available. NL_CONVERGENCE_ERROR: Occurs if the algorithm cannot converge within the allowed number of iterations.

Example

The following example illustrates how to find the minimum of Rosenbrock's function using this BFGS solver.

program example
    use nonlin_optimize, only : bfgs
    use nonlin_core, only : fcnnvar, fcnnvar_helper, iteration_behavior
    implicit none
 
    ! Local Variables
    type(bfgs) :: solver
    type(fcnnvar_helper) :: obj
    procedure(fcnnvar), pointer :: fcn
    real(real64) :: x(2), fout
    type(iteration_behavior) :: ib
 
    ! Initialization
    fcn => rosenbrock
    call obj%set_fcn(fcn, 2)
 
    ! Define an initial guess - the solution is (1, 1)
    call random_number(x)
 
    ! Call the solver
    call solver%solve(obj, x, fout, ib)
 
    ! Display the output
    print '(AF8.5AF8.5A)', "Rosenbrock Minimum: (", x(1), ", ", x(2), ")"
    print '(AE9.3)', "Function Value: ", fout
    print '(AI0)', "Iterations: ", ib%iter_count
    print '(AI0)', "Function Evaluations: ", ib%fcn_count
contains
    ! Rosenbrock's Function
    function rosenbrock(x) result(f)
        real(real64), intent(in), dimension(:) :: x
        real(real64) :: f
        f = 1.0d2 * (x(2) - x(1)**2)**2 + (x(1) - 1.0d0)**2
    end function
end

The above program yields the following output:

Rosenbrock Minimum: ( 1.00000,  0.99999)
Function Value: 0.200E-10
Iterations: 47
Function Evaluations: 70

See Also

• Wikipedia - BFGS Methods
• Wikipedia - Quasi-Newton Methods
• minFunc

Implements nonlin_core::equation_optimizer.

Definition at line 488 of file nonlin_optimize.f90.

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

• D:/Code/nonlin/src/nonlin_optimize.f90