       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
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

```

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