| Library: | nummath |
| See also: | nmgolden nmbracket nmlinminder nmcongrad nmbrentder |
| Quantlet: | nmlinminder | |
| Description: | Finds a minimum of func along the direction "direc" from x0 (using derivatives of func) |
| Usage: | lmin = nmlinminder(func,fder,x0,direc) | |
| Input: | ||
| func | name of function (string) whose minimum is to be found. The function should have just one parameter x (vector n x 1). As a result, the function should return scalar. | |
| fder | name of function (string) computing the gradient of func; it should return n x 1 vector. if empty, nmgraddiff will be used for computing the gradient | |
| x0 | n x 1 vector, starting point for the line minimization | |
| direc | n x 1 vector, direction vector of a line for the line minimization | |
| Output: | ||
| lmin.xlmin | n x 1 vector, minimum of func on the line x0 + span{direc} | |
| lmin.flmin | scalar, minimum function value on the line, f(xlmin) | |
| lmin.moved | n x 1 vector, vector displacement during line minimization, moved = xlmin - x0 | |
library("nummath")
;
; definition of function
;
proc(p)=ftion(x)
p = x[1,]^2 + 3*(x[2,]-1)^2
endp
;
lmin = nmlinminder("ftion","",#(2,2),#(0,1))
lmin
;
; minimization for x1 = 2, x2 = 2 + t
Contents of lmin.xlmin [1,] 2 [2,] 1 Contents of lmin.flmin [1,] 4 Contents of lmin.moved [1,] 0 [2,] -1
library("nummath")
;
; definition of function
;
proc(p)=ftion(x)
p = x[1,]^2 + 3*(x[2,]-1)^2
endp
;
lmin = nmlinminder("ftion","",#(1,2),#(1,-1))
lmin
;
; minimization for x1 = 1 + t, x2 = 2 - t
Contents of lmin.xlmin [1,] 1.5 [2,] 1.5 Contents of lmin.flmin [1,] 3 Contents of lmin.moved [1,] 0.5 [2,] -0.5