[scilab-Users] false results in Rosenbrock equation

[Michaël Baudin]

Your test case allowed me to a bug with respect to the management of the 
output function in the case of Box's algorithm. I reported it at :

http://bugzilla.scilab.org/show_bug.cgi?id=8805

Regards,

Michaël

Le 18/01/2011 09:19, Michaël Baudin a écrit :
> Hi Paul,
>
> The status of the optimization is not good when the parameters are 
> left to the default values :
>
> -->neldermead_get(nm,"-status")
>  ans =
> maxfuneval
>
> This means that the maximum number of function evaluations where 
> reached before the convergence was attained. All we need to do is to 
> increase the maximum number of function evaluations. In order to get 
> even closer to the optimum, we must also increase the number of 
> iterations.
>
> nm = neldermead_configure(nm,"-maxfunevals",200);
> nm = neldermead_configure(nm,"-maxiter",200);
>
> Once done, I get :
>
> -->xopt = neldermead_get(nm,"-xopt")
>  xopt  =
>     1.0035954
>     1.0073491
>
> This is quite a difficult case for Nelder-Mead's algorithm. The 
> simplex has to go through a long curved valley before reaching the 
> zone where the function begins to behave as a quadratic function.
>
> Rosenbrock's function has only one global minimum, at x=[1,1]. The 
> point x=[-1,1] is not a minimum.
>
> This is easy to check with Scilab. First, let us define the function.
>
>     function [f,G,H] = rosenbrock(x)
>         f = 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;
>
>         // Calculation of the gradient G vector
>         G(1) = -400*x(1)*(x(2) - x(1)^2) - 2*(1 - x(1));
>         G(2) = 200*(x(2) - x(1)^2);
>
>         // Calculation of the Hessian matrix
>         H(1,1) = -400*x(2) + 1200*x(1)^2 + 2;
>         H(1,2) = -400*x(1);
>         H(2,1) = -400*x(1);
>         H(2,2) = 200;
>     endfunction
>
> We get at x= [1,1] :
>
> -->[f,G,H] = rosenbrock([1,1])
>  H  =
>     802.  - 400.
>   - 400.    200.
>  G  =
>     0.
>     0.
>  f  =
>     0.
>
> This means that the gradient is zero, implying that the first order 
> conditions for unconstrained optimality are satisfied. Moreover, the 
> eigenvalues of the Hessian matrix are positive, as shown below :
>
> -->spec(H)
>  ans  =
>     0.3993608
>     1001.6006
>
> This implies that the local curvature of the Rosenbrock function is 
> positive : x* is indeed a minimum.
>
> Now, at x=[-1,1], we get :
>
> -->[f,G,H] = rosenbrock([-1,1])
>  H  =
>     802.    400.
>     400.    200.
>  G  =
>   - 4.
>     0.
>  f  =
>     4.
>
> The gradient is nonzero, which means that the first order optimality 
> conditions are not satisfied at x=[-1,1]. Rosenbrock's function is a 
> sum of squares.
>
> Best regards,
>
> Michaël
>
>
> Le 17/01/2011 11:18, Carrico, Paul a écrit :
>> Dear all
>> In the Rosenbrock equation it is well known the 2 minima are (1,1) 
>> and (-1,1) ; in the attached where I want to test several 
>> optimization macros (and basic &particular functions) I've a 
>> different result as descibed herebellow : is there a mistake in the 
>> input file or does something go wrong ?
>> Please note the functions inputs are as general as possible to be 
>> used with the different macros (fminsearch, optim and so on)
>> Paul
>> #################################################################"
>>     - X1 optimized = 0.229978
>>     - X2 optimized = 0.0240434
>> --------------------------------------------------------------------------------
>>
>>
>> Le présent mail et ses pièces jointes sont confidentiels et destinés à la personne ou aux personnes visée(s) ci-dessus. Si vous avez reçu cet e-mail par erreur, veuillez contacter immédiatement l'expéditeur et effacer le message de votre système. Toute divulgation, copie ou distribution de cet e-mail est strictement interdite.
>>
>> This email and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. If you have received this email in error, please contact the sender and delete the email from your system. If you are not the named addressee you should not disseminate, distribute or copy this email.
>>
>>
>
>
> -- 
> Michaël Baudin
> Ingénieur de développement
> michael.baudin at scilab.org
> -------------------------
> Consortium Scilab - Digiteo
> Domaine de Voluceau - Rocquencourt
> B.P. 105 - 78153 Le Chesnay Cedex
> Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94
>


-- 
Michaël Baudin
Ingénieur de développement
michael.baudin at scilab.org
-------------------------
Consortium Scilab - Digiteo
Domaine de Voluceau - Rocquencourt
B.P. 105 - 78153 Le Chesnay Cedex
Tel. : 01 39 63 56 87 - Fax : 01 39 63 55 94


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20110118/41d1fcd7/attachment.htm>