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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 20:17:43 +0000 (UTC)
Organization: National Research Council Canada - Conseil national de rechereches Canada
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In article <Xns9A419793662B6scottseidmanmindspri@130.133.1.4>,
Scott Seidman  <namdiesttocs@mindspring.com> wrote:
>roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in news:fopvio$2l2$1
>@canopus.cc.umanitoba.ca:

>>  The original poster requires an algorithm
>> which is guaranteed to find the global minima of an arbitrary 
>> black-box function of three parameters. Is that something that
>> people do "every day" ?

>As a matter of fact, yes.  One approach is to pick a handful of intial 
>guesses across the solution space, and perform the optimization starting 
>from each of them, and see which gives the best answer.  This is done every 
>day (engineering vs. math), and its poor practice to assume that your error 
>function might not get stuck in a global minimum.  

And we have exactly what assurance that the original poster's
MyFun is not at heart the negative of a Dirac Delta Function?
Pick an integer at random for the location of the delta. The
probability that the magnitude of the integer is less than
any particular value (e.g, 2^63-1) is zero, since there are
a finite number of integers in that absolute value range but an
infinite number of values outside of that range. And yet you expect
that your routines would be able to locate that one integer?


>He doesn't need an algorithm guaranteed to find the global minumum, he 
>needs to find the global minimum.  Again, many unconstrained optimization 
>problems are like this.

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.
-- 
  "To all, to each! a fair good-night,
   And pleasing dreams, and slumbers light"   -- Sir Walter Scott