looking inside FindMininum
- To: mathgroup at smc.vnet.net
- Subject: [mg29304] looking inside FindMininum
- From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
- Date: Tue, 12 Jun 2001 04:18:22 -0400 (EDT)
- Organization: Universitaet Regensburg
- Sender: owner-wri-mathgroup at wolfram.com
Dear Mathematica Gurus, I would like to minimize a function f[x,y]with respect to the arguments (x,y). The special problem ist that the simple y = 1-x.x > 0 where x is (x1,x2...,xn) must hold. I do this by minimizing f[x,y] + barrier[1-x.x] where barrier is a linear function of 1-x.x and grows if y approaches 0 or becomes < 0: barrier[x_,z_]:=If[#<z,10(1-#/z),0.0]&[1-x.x]; I. e. barrier > 0 if 1-x.x < z. Where z is a small positive number. z is set to a small number when the optimization start, but should approach 0 in the course of the Optimization routine in order to avoid distortions of the search. I would like to decrease z after every optimization step. But in order to do this I have to ask FindMininum for the number of steps. Until now I do this by z=0.1 FindMinimum[f[y,x]+barrier[1x.x,z*=decrement],...] but this is very unsatisfactory, because z is decremented every time when f[]+barrier[] is evaluated. I would like to adjust z in a more sophisticated way. But this is possible only if there is any way to get more information out of FindMininum, for example number of iterations etc. Is there any way to milk FindMiniumum? By the way: derivatives of f[y,x] cannot be computed. Thus I provide two starting values for every x and FindMinimum use a derivative-free method. Thank you and best regards, Johannes Ludsteck <><><><><><><><><><><><><><><><><><> Johannes Ludsteck Institut fuer Volkswirtschaftslehre Universitaet Regensburg Universitaetsstrasse 31 93053 Regensburg Tel +49/0941/943-2741