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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