multidimenstional minimization without df.

[Alxneit-Kamber Ivo]

On Tue, 2008-01-22 at 09:06 -0500, Toan T Nguyen wrote:
> Hi,
> 
> I'd like to locate the minimum point of a function f(x_i) of n variables 
> x_i. It's very non trivial to calculate the df/dx_i. Can I use conjugate 
> gradian method without this df(x_i) information ?
> 
> This page in the manual 
> http://www.gnu.org/software/gsl/manual/html_node/Multimin-Algorithms.html
> 
> doesn't list gsl_multimin_fminimizer_conjugate_fr as a type of 
> minimizer. It has
> 	gsl_multimin_fdfminimizer_conjugate_fr
> but no
> 	gsl_multimin_fminimizer_conjugate_fr
> 
> Any help would be appreciated.
> 
> Thanks,
> Toan

hi,

no, the conjugate gradient method needs the derivatives (to calculate
the gradient). thus, there can be no minimizer
gsl_multimin_fminimizer_conjugate_fr (fdf minimizer: you supply f(x) AND
df/dx. f minimuzer: you only supply f(x)). so, either you are able to
supply the derivatives or you will end up with
gsl_multimin_fminimizer_nmsimplex that needs no derivatives.

i often use gsl_multimin_fminimizer_nmsimplex to fit parameters of
rather complex simulations. here the function evaluation takes up to a
few minutes and i do not have access to the derivatives. note, that i
have applied following patch
http://www.network-theory.co.uk/download/gslextras/SimplexImproved/
(otherwise the minimizer most often gets stuck at the starting point)
and i scale the parameters in a way to make their numerical values
similar (i usually divide by their initial values).

-- 
Dr. Ivo Alxneit
Laboratory for Solar Technology   phone: +41 56 310 4092
Paul Scherrer Institute             fax: +41 56 310 2688
CH-5232 Villigen                   http://solar.web.psi.ch
Switzerland                   gnupg key: 0x515E30C7
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