XploRe Help : nelmin

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Group:	Optimizer
See also:	bfgs

Function:		nelmin
Description:		nelmin searchs for a minimum of a function. In each iteration step the function is evaluated at a simplex consisting of p+1 points. The simplex contracts until the variance of the evaluated function values is less than eps (or the maximal number of iterations is reached).

Reference(s):

Nelder, J. A. and Mead, R. (1965). A Simplex Method for Function Minimization. "Computer J.", vol 7,308-313.

Usage:	`x = nelmin (x0, f, maxiter {,eps , step})`
Input:
	`x0`	p x n matrix with n starting vectors
	`f`	text, name of the procedure where the function is defined
	`maxiter`	integer, maximal number of iterations
	`eps`	scalar
	`step`	scalar, lenght of initial simplex
Output:
	`x.minimum`	p x n matrix with the n minima
	`x.iter`	number of iterations
	`x.converged`	1 if the algorithm has converged with every starting vector and 0 if it has not

Note:

maxiter should be greater then the number of dimensions p.

Example:

proc(y) = f(x) y = sum(x^2) endp x0 = #(1,1,1)~#(1,2,3) nelmin(x0, "f", 100, 1.0e-6)

Result:

Contents of nelmin.minimum



[1,]  0.017404 -0.02019

[2,] -0.0070216  0.022459

[3,]  0.016622  0.0042336

Contents of nelmin.iter



[1,]       53

Contents of nelmin.converged



[1,]        1