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From: roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson)
Newsgroups: comp.soft-sys.matlab
Subject: Re: Find Minimum
Date: Mon, 11 Feb 2008 20:55:08 +0000 (UTC)
Organization: National Research Council Canada - Conseil national de rechereches Canada
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In article <Xns9A419D4C96F57scottseidmanmindspri@130.133.1.4>,
Scott Seidman  <namdiesttocs@mindspring.com> wrote:
>roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in news:foqah7$fds$1
>@canopus.cc.umanitoba.ca:

>> The original poster did not ask for an engineering "close enough"
>> solution: the original poster asked to find the parameters that minimize
>> (over an infinite domain) the un-examinable function. You can
>> graph all the finite subsets you want, but you cannot hide from
>> infinity.

>So, once again you assert that there is no way to optimize an unconstrained 
>3-parameter problem with global minima.  Many minimization problems are not 
>looking for a microscopic dirac in infinite 3D.  I suppose we could assume 
>that's that kind of function the OP is presenting, or we could assume that 
>his problem is not of that sort, and is much more mundane.  

Assuming that the original poster's problem is "not of that sort"
and to be globally optimizable with any fixed algorithm is to place
(mathematically) quite large restrictions on the details of the
black-box function, violating the original poster's assertion that
nothing was known of the function beyond how to evaluate it.

Your claim that the original poster's problem *as originally stated*
could be solved by a minimization algorithm was wrong.

Even if you had an algorithm that (for example) after five
function evaluations was able to predict a parameter combination that
was unsurpassed in another billion explorations of the parameter
space, then because of the black-box nature of the function,
you would never be sure that you had found the global minima
(which might take quadrillions of evaluations to find a better minima).
You might perhaps appear to converge very quickly, but if it is a
black box problem with no known constraints on its internal contents,
then you never know when to stop evaluating to be sure you had the
global minima.
-- 
  "You can't hit what you can't see."  -- Walter "The Big Train" Johnson