Re: [Bug-gsl] One dimensional minimum finding

[Brian Gough]

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/