XploRe Help : bfgs

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:	nelmin

Function:		bfgs
Description:		Searches the global minimum of a function.

Reference(s):

Bulirsch, R. and Stoer, J. (1980). "Introduction to Numerical Analysis", p. 302, Springer-Verlag. Schwetlick, H. (1979). "Numerische Loesung Nichtlinearer Gleichungen", p.187, VEB Deutscher Verlag Wissenschaften.

Usage:	`x = bfgs (x0, f, df, maxiter {,eps, gamma})`
Input:
	`x0`	n x 1 vector of starting value
	`f`	text, name of the procedure where the function is defined
	`df`	text, name of the procedure where the derivative of the function is defined
	`maxiter`	integer, maximal number of iterations
	`eps`	scalar, bfgs stops, if df(x_i) < eps (i=1...n) (default = 1.0e-03)
	`gamma`	scalar, starting value for linesearch (default = 1.0)
Output:
	`x.minimum`	n x 1 vector, coordinates of the minimum found
	`x.iter`	integer, number of iterations needed
	`x.converged`	1 if the algorithm has converged and 0 if it has not

Example:

proc(y) = f(x) y = sum((x-2)^2) endp proc(y) = df(x) y = 2*(x-2) endp x0=#(1,1,1) bfgs(x0,"f","df",50) //alternative bfgs may be called with text variables f1="f" ; define f as text variable containing string "f1" bfgs(x0, f1, "df", 50)

Result:

Contents of bfgs.minimum
[1,]        2
[2,]        2
[3,]        2
Contents of bfgs.iter
[1,]        1
Contents of bfgs.converged
[1,]        1
Contents of bfgs.minimum
[1,]        2
[2,]        2
[3,]        2
Contents of bfgs.iter
[1,]        1
Contents of bfgs.converged
[1,]        1