numerical::QuasiNewton< N, Function, T, Point > Class Template Reference

The quasi-Newton BFGS method. More...

#include <QuasiNewton.h>

Inheritance diagram for numerical::QuasiNewton< N, Function, T, Point >:

List of all members.

Accessors.
const function_type &	function () const
	Return a constant reference to the objective function.
int	num_function_calls () const
	Return the number of function calls required to find the minimum.
number_type	x_tolerance () const
	Return the x tolerance for convergence.
number_type	gradient_tolerance () const
	Return the gradient tolerance for convergence.
static int	dimension ()
	Return the dimension, N.
Public Types
typedef base_type::function_type	function_type
	The function type.
typedef base_type::number_type	number_type
	The number type.
typedef base_type::point_type	point_type
	A point in N dimensions.
Public Member Functions
Constructors etc.
The default constructor, the copy constructor and the assignment operator are not implemented.
	QuasiNewton (const function_type &function, const number_type x_tolerance=4 *std::numeric_limits< number_type >::epsilon(), const number_type gradient_tolerance=4 *std::numeric_limits< number_type >::epsilon(), const int max_function_calls=10000)
	Construct from the objective function.
virtual	~QuasiNewton ()
	Destructor.
Minimization.
void	find_minimum (point_type &x, number_type &value, int &num_iterations, number_type max_step=0, const number_type x_tolerance=0, const number_type gradient_tolerance=0)
	Find the minimum.
void	find_minimum (point_type &x)
	Find the minimum.
Manipulators.
void	set_max_function_calls (const int max_function_calls)
	Set the maximum number of function call allowed per optimization.
void	reset_num_function_calls ()
	Reset the number of function calls to zero.
void	set_x_tolerance (const number_type x_tolerance)
	Set the x tolerance for convergence.
void	set_gradient_tolerance (const number_type gradient_tolerance)
	Set the gradient tolerance for convergence.
Protected Member Functions
Calling the objective function.
Functionality inherited from Opt.
number_type	evaluate_function (const point_type &x)
	Evaluate the objective function and return the result.
void	evaluate_gradient (const point_type &x, point_type &gradient)
	Evaluate the gradient.
void	evaluate_numeric_gradient (const point_type &x, point_type &gradient, const number_type delta=0.0)
	Numerically evaluate the gradient.

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Detailed Description

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>
class numerical::QuasiNewton< N, Function, T, Point >

The quasi-Newton BFGS method.

Parameters:

	N	is the problem dimension.
	Function	is the functor to minimize.
	T	is the number type. By default it is Function::result_type;
	Point	is the point type. By default it is Function::argument_type;

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Member Function Documentation

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>

number_type numerical::QuasiNewton< N, Function, T, Point >::evaluate_function

(

const point_type &

x

)

[inline, protected]

Evaluate the objective function and return the result.

Increment the count of the number of function calls.

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>

void numerical::QuasiNewton< N, Function, T, Point >::evaluate_gradient	(	const point_type &	x,
		point_type &	gradient
	)			[inline, protected]

Evaluate the gradient.

Increment the count of the number of function calls.

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>

void numerical::QuasiNewton< N, Function, T, Point >::evaluate_numeric_gradient	(	const point_type &	x,
		point_type &	gradient,
		const number_type	delta = 0.0
	)			[inline, protected]

Numerically evaluate the gradient.

Increment the count of the number of function calls.

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>

void numerical::QuasiNewton< N, Function, T, Point >::find_minimum

(

point_type &

x

)

[inline]

Find the minimum.

Parameters:

x

The input value is the starting point. The output value is the minimum point found.

template<int N, class Function, typename T = typename Function::result_type, typename Point = typename Function::argument_type>

void numerical::QuasiNewton< N, Function, T, Point >::find_minimum	(	point_type &	x,
		number_type &	value,
		int &	num_iterations,
		number_type	max_step = 0,
		const number_type	x_tolerance = 0,
		const number_type	gradient_tolerance = 0
	)

Find the minimum.

Parameters:

	x	The input value is the starting point. The output value is the minimum point found.
	value	is the value of the objective function at the minimum point.
	num_iterations	is the number of iterations of the method.
	max_step	is the maximum step used in the line search.
	x_tolerance	is the x tolerance for convergence. The function returns if the line search takes a smaller step than this.
	gradient_tolerance	is the gradient tolerance for convergence. The function returns if the magnitude of the gradient falls below this value.

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

• QuasiNewton.h

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