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## Re: [Bug-gsl] One dimensional minimum finding

 From: Ionut Georgescu Subject: Re: [Bug-gsl] One dimensional minimum finding Date: Tue, 13 Sep 2005 21:55:25 +0200 User-agent: Mutt/1.5.10i

On Tue, Sep 13, 2005 at 05:17:44PM +0100, Brian Gough wrote:
> Ionut Georgescu writes:
>  > The minimization algorithms quit if the original estimation of the
>  > position of the minimum is not so good, that is if
>  >
>  > f(a) > f(x) < f(b)
>  >
>  > does not hold.  I find this too hard a condition because even if the
>  > function is monotone, than it still has a minimum, either f(a) or f(b).
>
> Hello,
> The algorithms find a local minimum (i.e. f'(x)=0 f''(x)>0 or similar) as
> opposed to a lowest value.  Hence the above condition is required.
>
>  > But this is not the real reason.  Sometimes it is very difficult to give
>  > a good guess of the minimum, even if we certainly know that there is
>  > one. I tried to improve my guess by running golden_section a few times
>  > before running brent, but it also failed at the above condition, which
>  > is common to all the algorithms.
>
> Unfortunately this is how the algorithm works.  If your initial
> bracket isn't valid, try generating a new point in the appropriate
> direction and discarding the opposite one until it is.

Hello Brian,

thank you, I have already done that. I have written a sort of golden
section algorithm which is able to improve my initial guess. I just
wished that somehow this could be possible by simply using GSL, without
the need to duplicate the code.

Anyway, please forget it. It would just bloat the library and we
certainly don't want that :-)

Greetings,
Ionut

PS I just realized, instead of rewriting from scratch, I could have just
copied gsl_min_fminimizer_set() and
gsl_min_fminimizer_set_with_values(), removed the unwanted lines and
used golden_section as needed :-)

--
***************
* Ionuţ Georgescu
* Max-Planck-Institut für Physik komplexer Systeme
* Noethnitzer Str. 38, D-01187 Dresden
* Phone: +49 (351) 871-2209
* Fax:   +49 (351) 871-1999

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