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Re: [Bug-gsl] One dimensional minimum finding
From: |
Brian Gough |
Subject: |
Re: [Bug-gsl] One dimensional minimum finding |
Date: |
Tue, 13 Sep 2005 17:17:44 +0100 |
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.
--
regards
Brian Gough
Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/