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From: Scott Seidman <namdiesttocs@mindspring.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Find Minimum
Date: 11 Feb 2008 20:47:53 GMT
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shapper <mdmoura@gmail.com> wrote in
news:fbffb731-d31b-4562-a193-2affe6006cf7@v17g2000hsa.googlegroups.com: 

> On Feb 11, 8:17 pm, rober...@ibd.nrc-cnrc.gc.ca (Walter Roberson)
> wrote:
>> In article <Xns9A419793662B6scottseidmanminds...@130.133.1.4>,
>> Scott Seidman  <namdiestt...@mindspring.com> wrote:
>>
>> >rober...@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
> 
> Hi,
> 
> I was thinking about my problem and let me simplify it so I can solve
> this.
> 
> Basically, the function does some calculation to evaluate a financial
> report.
> 
> Please, consider the new problem:
> 
> 1. All inputs will have a finite number or values, i.e:
> 
>    Input A: Integer value between 0 and 2000
>    Input B: Zero or Multiple of 10 between 0 and 200 -  0, 10, 20,
> 30, ..., 190, 200
>    Input C: Multiple of 0.01 between 0 and 1 - 0.01, 0.02, ... , 0.98,
> 0.99, 1
> 
> 2. The problem might have more than one minimum.
>    In this case I would like to get the global solution.
>    If no global solution is found then it would be interesting to get
> all local solutions to be compared ...
> 
>    Event getting the local solutions, when a global solution is found,
> might be interesting in this case.
> 
> Anyway, by setting all inputs to be finite how should I do this?
> 
> I think that was the biggest problem.
> 
> Thank You,
> Miguel
> 
> 
> 

There you go!

Depending on how complex your function is, and how fast you need an 
answer, you might just choose to evaluate your function at all 4,000,000 
some-odd values in your parameter space.  That's a guaranteed solution.

-- 
Scott
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