Newton Search. More...

#include <itpp/optim/newton_search.h>

Public Member Functions
	Newton_Search ()
	Default constructor.

	~Newton_Search ()
	Destructor.

void	set_function (double(*function)(const vec &))
	Set function pointer.

void	set_gradient (vec(*gradient)(const vec &))
	Set gradient function pointer.

void	set_functions (double(function)(const vec &), vec(gradient)(const vec &))
	Set both function and gradient function pointers.

void	set_start_point (const vec &x, const mat &D)
	Set start point `x` for search and approx inverse Hessian at `x`.

void	set_start_point (const vec &x)
	Set start point `x` for search.

vec	get_solution ()
	Get solution, function value and gradient at solution point.

bool	search ()
	Do the line search.

bool	search (vec &xn)
	Do the line search and return solution.

bool	search (const vec &x0, vec &xn)
	Set starting point, do the Newton search, and return the solution.

void	set_stop_values (double epsilon_1, double epsilon_2)
	Set stop criterion values.

double	get_epsilon_1 ()
	Return stop value rho.

double	get_epsilon_2 ()
	Return stop value beta.

void	set_max_evaluations (int value)
	Set max number of function evaluations.

int	get_max_evaluations ()
	Return max number of function evaluations.

void	set_initial_stepsize (double value)
	Set max stepsize.

double	get_initial_stepsize ()
	Return max number of iterations.

void	set_method (const Newton_Search_Method &method)
	Set Line search method.

double	get_function_value ()
	get function value at solution point

double	get_stop_1 ()
	get value of stop criterion 1 at solution point

double	get_stop_2 ()
	get value of stop criterion 2 at solution point

int	get_no_iterations ()
	get number of iterations used to reach solution

int	get_no_function_evaluations ()
	get number of function evaluations used to reach solution

void	enable_trace ()
	enable trace mode

void	disable_trace ()
	disable trace

void	get_trace (Array< vec > &xvalues, vec &Fvalues, vec &ngvalues, vec &dvalues)

Detailed Description

Newton Search.

Newton or Quasi-Newton optimization method that try to minimize the objective function $f(\mathbf{x})$ given an initial guess $\mathbf{x}$ .

The search is stopped when either criterion 1:

$\left\| \mathbf{f}'(\mathbf{x})\right\|_{\infty} \leq \varepsilon_1$

or criterion 2:

$\left\| d\mathbf{x}\right\|_{2} \leq \varepsilon_2 (\varepsilon_2 + \| \mathbf{x} \|_{2} )$

is fulfilled. Another possibility is that the search is stopped when the number of function evaluations exceeds a threshold (100 per default).

The default update rule for the inverse of the Hessian matrix is the BFGS algorithm with $\varepsilon_1 = 10^{-4}$ an $\varepsilon_2 = 10^{-8}$ .

Definition at line 72 of file newton_search.h.

Member Function Documentation

void itpp::Newton_Search::get_trace	(	Array< vec > &	xvalues,
		vec &	Fvalues,
		vec &	ngvalues,
		vec &	dvalues
	)

get trace outputs xvalues are the solutions of every iteration Fvalues are the function values ngvalues are the norm(gradient,inf) values dvalues are the delta values

Definition at line 311 of file newton_search.cpp.

References it_warning.

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

itpp/optim/newton_search.h
itpp/optim/newton_search.cpp

Public Member Functions

Detailed Description

Member Function Documentation