Optimizing math functions

[Robert Kern]

On 2009-05-24 07:42, Esmail wrote:
> Robert Kern wrote:
>>
>>
>> We have several bounded optimization routines in scipy.
>>
>> http://docs.scipy.org/doc/scipy/reference/optimize.html
>
> Hi Robert,
>
> Thanks for the lead .. I briefly looked at the documentation, but
> before I dig into this more deeply 2 quick questions:
>
> 1. Will is also allow me to maximize a function (I only saw minimum)?

Already answered.

> 2. Will it give me the global minima/maxima?

No, they are local optimizers.

> I only ask because I got all excited to see that R has an optimize
> function but unfortunately it can not deal with multi-modal functions.
> I am trying to come up with some complex test cases for a genetic
> algorithm I'm working with, both for functions using f(x) and f(x,y) over a
> variety of intervals so I would like to have a way to verify results for
> more challenging functions.

You may want to consider using artificial functions with known optima. Here is a 
paper from the ACM Transactions on Mathematical Software doing such:

   http://portal.acm.org/citation.cfm?id=962444
   http://wwwinfo.deis.unical.it/~yaro/GKLS.html
   http://www.netlib.org/toms/829

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco