[R] optimized value worse than starting Value

[Hans W Borchers]

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
>