Nelder - Mead Algorithm

[Michaël Baudin]

Hi,

Several users requested a way to perform optimizations in Scilab with a
tool similar to the fminsearch Matlab command.
The SEP in attachment is a proposal for such a tool.

A prototype is currently available, with the following features:
* emulates the fminsearch command with the same numerical
parameters and algorithm as Matlab's fminsearch,
* Box's complex method with bound constraints and non linear
inequality constraints,
* oriented simplex restart (and variants) with automatic
stagnation detection by O'Neill or Kelley criteria,
* many other features and options...

Numerical experiments show that the current prototype is able
to reproduce exactly the behaviour of Matlab's fminsearch, including
the initial simplex, the intermediate simplices and the final simplex
at optimum. It allows to reproduce the behaviour analysed by Kelley
on the Mc Kinnon couterexample. It behaves reasonably well on
problems with bounds and non linear inequality constraints.

Several improvements are possible on this algorithm :
comments and suggestions are welcome !

Best regards,

Michaël Baudin

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