Nelder - Mead Algorithm

[Collette Yann]

Look OK for me.
The thing very important to me is to be able to initialise fminsearch 
with our own simplex.
fminsearch has not such a functionnality and if inputs variables have 
very different scale of variations, then the initial simplex, as created 
by fminsearch, will be degenerated.
The Kelley restart is a plus. It allows to accelerate in some cases the 
convergence of the nelder and mead method.

The optimization method implemented in my simplex-2.0 toolbox is a 
little bit special. It allows to "record" the state of the simplex and 
stop to ask the user to do a computation.
With the step_nelder_mead, all the call to the objective function are 
done by the user.
With the optim_nelder_mead, you ship the objective function to the 
method and optim_nelder_mead call by himself the objective function

I will add somes tests in the simplex-2.0 toolbox. I've got a lot of 
test problems ...

YC

Michaël Baudin a écrit :
> 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
>