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From: spellu...@mathematik.tu-darmstadt.de (Peter Spellucci)
Newsgroups: comp.lang.fortran,sci.math.num-analysis
Subject: Re: Nonlinear solvers for expensive functions
Date: 12 Mar 2002 10:37:14 GMT
Organization: TU Darmstadt, Fachbereich Mathematik
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In article <204e7041.0203110920.3e8f2...@posting.google.com>,
 adr...@bjahouston.com (Adrian Ferramosca) writes:
|> I have a multidimensional nonlinear problem to solve where the
|> function evaluations are very expensive and the number of variables
|> can be large.  Therefore derivative based solvers (user-supplied or
|> numerical) are not an option.  I am using a Wegstein type solver at
|> present, but are there any other solutions methods out there which can
|> handle these types of problems?  I tried implementing GDEM from the
|> original paper but couldn't get it working.
|> 
|> Adrian

until now i believed to know something about optimization but must state that
neither I know was a wegstein solver is nor what GDEM.
It would be a good idea not to assume that others know your slang. 
you did say nothing about the nature of your function evaluations. as others
correctly stated, the use of gradient (and even Hessian) information becomes
more important then the function evaluation is costly and dimension is large.
(what is "large" for you? n=50000?) 
I assume that  your function evaluation come from a software (or even worse
hardware) blackbox, and in this case indeed automatic differentiation is not
possible. If you have an algorithm in the form of a subprogram, then automatic
differentiation is the way to go. 
but here come some info's, which possibly might be of help
peter

Jones, Donald R.; Schonlau, Matthias; Welch, William J.
Efficient global optimization of expensive black-box functions. (English)
[J] J. Glob. Optim. 13, No.4, 455-492 (1998). [ISSN 0925-5001]

Toropov, V.V.
Multipoint approximation method in optimization problems with 
expensive function values. (English)
[CA] Computational systems analysis, Proc. 4th Int. Symp. Syst. Anal. 
Simulation, Berlin/Ger. 1992, 207-212 (1992).


Schagen, I.P.
Stochastic interpolation applied to the optimisation of expensive 
objective functions. (English)
[CA] Computational statistics, Proc. 4th Symp., Edinburgh 1980, 362-367 (1980).