Re: [Help-gsl] On conjugate gradient algorithms in multidimentional minimisation problems.

[Christian MOENNE-LOCCOZ]

Few month ago, I had to try the gsl conjugate gradient algorithms.
On small fonctions, I had no problem. But a friend of mine give me that fonction
:

double
fonction(const Vecteur& x) const {
        Double valeur =
                 100.0 * (x[1] - x[0]*x[0]) * (x[1] - x[0]*x[0]) + (1.0 - x[0]) 
* (1.0 - x[0])
+
                  90.0 * (x[3] - x[2]*x[2]) * (x[3] - x[2]*x[2]) + (1.0 - x[2]) 
* (1.0 - x[2])
+
                  10.1 * (x[1] - 1.0) * (x[1] - 1.0) + 10.1 * (x[3] - 1.0) * 
(x[3] - 1.0) +
                  19.8 * (x[1] - 1.0) * (x[3] - 1.0);
        return valeur;
}

void
gradient(const Vecteur &x, Vecteur& g) const {
        g[0] =  -2.0 * 100.0 * (x[1] - x[0]*x[0])* 2.0 * x[0]
                - 2.0 * (1.0 - x[0]);
        g[1] =  100.0 * (x[1] - x[0]*x[0]) +  10.1 * 2.0 * (x[1] - 1.0) +
                 19.8 * (x[3] - 1.0);
        g[2] =  -2.0 * 90.0 * (x[3] - x[2]*x[2]) * 2.0 * x[2] -  2.0 * (1.0 
-x[2]);
        g[3] =  2.0 * 90.0 * (x[3] - x[2]*x[2]) + 10.1 * 2.0 * (x[3] - 1.0) +
                 19.8 * (x[1] - 1.0);


It has only 4 dimensions, but the GSL algorithm alway fails to find the minimum
at (1, 1, 1, 1).
It's seems to be same erreur message as your : "iterations not progressing
toward a solution".

My friend program the classic conjugate gradient algorithm on Mathlab (to choose
the direction), but then using the Mathlab algorithm for line minimisation. Then
it work perfectly with my special fonction.

I concluded that the gsl algorithm could probably be improved. But I'm not a
mathematician.

--
locnet