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From: braner@batcomputer.UUCP
Newsgroups: sci.math.stat,comp.sources.wanted
Subject: Re: all purpose minimizer
Message-ID: <158@batcomputer.tn.cornell.edu>
Date: Wed, 11-Feb-87 00:49:23 EST
Article-I.D.: batcompu.158
Posted: Wed Feb 11 00:49:23 1987
Date-Received: Thu, 12-Feb-87 00:01:14 EST
References: <1631@cit-vax.Caltech.Edu>
Reply-To: braner@batcomputer.UUCP (braner)
Organization: Theory Center, Cornell University, Ithaca NY
Lines: 19
Xref: utgpu sci.math.stat:48 comp.sources.wanted:477
Summary: Global is hard.  I use POWELL from Numerical Recipes.

[]

GLOBAL minimization is a very hard problem.  How do you avoid missing
a very narrow trench?  Check all points on a very fine grid? In 20
dimensions?

Pessimism aside, I use the routine called 'Powell', in the book 'Numerical
Recipes' (by Press et al, Cambridge U. Press, 1986).  It does not use
derivatives, and seems reasonably robust for the  very nonlinear  functions
of many (from 3 to 20) variables I try to minimize.  (I use it for
maximum-likelihood estimation of parameters.)   (I had to modify it a bit,
though: changed the parametrization in 'Linmin' so that the best guess of
the minimum is at 1, not 0.  If it happens to be at 0, 'Brent' iterates
for a long time since it measures _relative_ error.  Also note that the
order of the parameters in the initial direction set is VERY critical for
successful use of the algorithm, and the best order depends on your
specific function!)

- Moshe Braner