itpp::Line_Search Class Reference
[Numerical Optimization Module]

Line Search. More...

#include <newton_search.h>

List of all members.

Public Member Functions

Line_Search ()

Default constructor.

~Line_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, double F, const vec &g, const vec &h)

Set start point for search.

void get_solution (vec &xn, double &Fn, vec &gn)

Get solution, function value and gradient at solution point.

bool search ()

Do the line search.

bool search (vec &xn, double &Fn, vec &gn)

Do the line search and return solution.

bool search (const vec &x, double F, const vec &g, const vec &h, vec &xn, double &Fn, vec &gn)

Set starting point, do the line search, and return the solution.

double get_alpha ()

return alpha at solution point, xn = x + alpha h

double get_slope_ratio ()

return the slope ratio at solution poin, xn

int get_no_function_evaluations ()

return number of function evaluations used in search

void set_stop_values (double rho, double beta)

Set stop criterion values.

double get_rho ()

Return stop value rho.

double get_beta ()

Return stop value beta.

void set_max_iterations (int value)

Set max number of iterations.

int get_max_iterations ()

Return max number of iterations.

void set_max_stepsize (double value)

Set max stepsize.

double get_max_stepsize ()

Return max number of iterations.

void set_method (const Line_Search_Method &method)

Set Line search method.

void enable_trace ()

enable trace mode

void disable_trace ()

disable trace

void get_trace (vec &alphavalues, vec &Fvalues, vec &dFvalues)

Detailed Description

Line Search.

The line search try to minimize the objective function $f(\mathbf{x})$ along the direction $\mathbf{h}$ from the current position $\mathbf{x}$ .

Hence we look at

$\varphi(\alpha) = f(\mathbf{x} + \alpha \mathbf{h})$

and try to find an $\alpha_s$ that minimizes $f$ .

Two variants are used. Either the soft line search (default) or the exact line search.

The soft line search stops when a point in the acceptable region is found, i.e.

$\phi(\alpha_s) \leq \varphi(0) + \alpha_s \rho \varphi'(0)$

and

$\varphi'(\alpha_s) \geq \beta \varphi'(0),\: \rho < \beta$

Default vales are $\rho = 10^{-3}$ and $\beta = 0.99$ .

The exact line search

$\| \varphi(\alpha_s)\| \leq \rho \| \varphi'(0) \|$

and

$b-a \leq \beta b,$

where $\left[a,b\right]$ is the current interval for $\alpha_s$ . Default vales are $\rho = 10^{-3}$ and $\beta = 10^{-3}$ .

The exact line search can at least in theory give the exact resutl, but it may require many extra function evaluations compared to soft line search.

Member Function Documentation

void itpp::Line_Search::get_trace	(	vec &	alphavalues,
		vec &	Fvalues,
		vec &	dFvalues
	)

get trace outputs alphavalues are the solutions of every iteration Fvalues are the function values dFvalues

References it_warning.

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


Public Member Functions
	Line_Search ()
	Default constructor.
	~Line_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, double F, const vec &g, const vec &h)
	Set start point for search.
void	get_solution (vec &xn, double &Fn, vec &gn)
	Get solution, function value and gradient at solution point.
bool	search ()
	Do the line search.
bool	search (vec &xn, double &Fn, vec &gn)
	Do the line search and return solution.
bool	search (const vec &x, double F, const vec &g, const vec &h, vec &xn, double &Fn, vec &gn)
	Set starting point, do the line search, and return the solution.
double	get_alpha ()
	return alpha at solution point, xn = x + alpha h
double	get_slope_ratio ()
	return the slope ratio at solution poin, xn
int	get_no_function_evaluations ()
	return number of function evaluations used in search
void	set_stop_values (double rho, double beta)
	Set stop criterion values.
double	get_rho ()
	Return stop value rho.
double	get_beta ()
	Return stop value beta.
void	set_max_iterations (int value)
	Set max number of iterations.
int	get_max_iterations ()
	Return max number of iterations.
void	set_max_stepsize (double value)
	Set max stepsize.
double	get_max_stepsize ()
	Return max number of iterations.
void	set_method (const Line_Search_Method &method)
	Set Line search method.
void	enable_trace ()
	enable trace mode
void	disable_trace ()
	disable trace
void	get_trace (vec &alphavalues, vec &Fvalues, vec &dFvalues)

itpp::Line_Search Class Reference [Numerical Optimization Module]

Public Member Functions

Detailed Description

Member Function Documentation

itpp::Line_Search Class Reference
[Numerical Optimization Module]