Barry Rowlingson <b.rowlingson <at> lancaster.ac.uk> writes:
>
> On Wed, Sep 8, 2010 at 1:35 PM, Michael Bernsteiner
> <dethlef1 <at> hotmail.com> wrote:
> >
> > Dear all,
> >
> > I'm optimizing a relatively simple function. Using optimize the optimized
> > parameter value is worse than the starting. why?
I would like to stress here that finding a global minimum is not as much
sorcery as this thread seems to suggest. A widely accepted procedure to
provably identify a global minimum goes roughly as follows
(see Chapt. 4 in [1]):
- Make sure the global minimum does not lie 'infinitely' for out.
- Provide estimations for the derivatives/gradients.
- Define a grid fine enough to capture or exclude minima.
- Search grid cells coming into consideration and compare.
This can be applied to two- and higher-dimensional problems, but of course
may require enormous efforts. In science and engineering applications it is at
times necessary to really execute this approach.
Hans Werner
[1] F. Bornemann et al., "The SIAM 100-Digit Challenge", 2004, pp. 79.
"In fact, a slightly finer grid search will succeed in locating the
proper minimum; several teams used such a search together with estimates
based on the partial derivatives of f to show that the search was fine
enough to guarantee capture of the answer."
> This looks familiar. Is this some 1-d version of the Rosenbrock
> Banana Function?
>
> http://en.wikipedia.org/wiki/Rosenbrock_function
>
> It's designed to be hard to find the minimum. In the real world one
> would hope that things would not have such a pathological behaviour.
>
> Numerical optimisations are best done using as many methods as
> possible - see optimise, nlm, optim, nlminb and the whole shelf of
> library books devoted to it.
>
> Barry
>
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