[scilab-Users] Probably a stupid question but...

[Yann Collette]

Sébastien Bihorel a écrit :
> Hi Yann,
>
> The installation worked just fine. I thank you again for your 
> explanations.
>
> Now, I would like to ask you a couple of more theoretical questions on 
> the algorithm implemented in the nm_init, step_nelder_mead or 
> optim_nelder_mead. I am not a mathematician and don't know much about 
> the theories, and the nuts and bolts of the Nelder-Mead algorithm 
> (this is probably a mistake!). My only concern, until recently, was 
> only to know how to use it in Matlab using the fminsearch function... 
> This function is nice for lay users because one doesn't have to care 
> about dealing with simplex objects.
> The simplex toolbox seem to require such objects to be created and 
> passed from one iteration to the other. From your documentation and 
> examples, it is my understanding that the simplex contain realizations 
> of the objective function at different places of the search space. Am 
> I correct here?
>
There are 2 versions of the simplex in this toolbox:
- optim_nelder_mead: this function takes as argument an objective 
function and some other parameters. All the computation are performed 
inside optim_nelder_mead. So, you just have to start optim_nelder_mead 
and get the result
- steip_nelder_mead: it's the same method as above, the big difference 
is that step_nelder_mead doesn't perform any objective function 
computation. Each time step_nelder_mead needs an objective function 
value, it stops, give back hand to the user who have to compute the 
needed objective function computation and then restart step_nelder_mead 
by giving the preceding state of step_nelder_mead and the requested 
objective function values.
> Another thing I am not clear about is whether or not the dimensions of 
> the simplex should be adapted to a specific problem. In the examples 
> you provide, the simplex f_init and f_current have a 3x1 dimension for 
> optimizing 2 parameters. Is that 3x1 dimension independent of the 
> number of parameters to optimize? Let's say my objective function is a 
> 'maximum likelihood function' of observations (n states observed at t 
> times) given a model dependent on m parameters and a residual 
> variability dependent on v parameters, what should be the size of the 
> simplex and how should it be calculated?
>
Normally, the X0 parameter is an initial simplex. You can compute it 
yourself or compute it using nm_init. So, the x0 dimensions are n x n+1 
(the documentation is wrong here. I will correct this ASAP).

For your problem, if you have n states at t times, you must transform 
you m x t matrix into a [mxt,1] vector and then use nm_init to compute a 
[mxt,mxt+1] initial simplex.

YC



-- 
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Yann COLLETTE
Software Development Engineer
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The Scilab Consortium
Digiteo Foundation
Domaine de Voluceau
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Phone: +33.1.39.63.57.82