nmsimplex iteration.

[picca <picca@synchrotron-soleil.Fr>]

Hello

I am using the simplex minimisation to solve a problem of
crystallography. The function to minimize is :
f = f(euler_x, euler_y, euler_z, a, b, c, alpha, beta, gamma);

in fact a, b, c, alpha, beta, gamma are the parameters of a triedra,
a, b, c, are the length of the sides and alpha, beta, gamma the angles
of the triedra.

for some combinations of alpha, beta, gamma , f(blabla...) = GSL_NAN.
So the simplex can not converge. If I return a really big number as it
was suggested in a previous thread of the mailing list, the simplex
must be contracted around the better corner. But it is not always
possible to obtain a valid contraction in one guess.

To be clear this simplex algorithm only work for a convex space. And
my problem is not convex.

Nevertheless if we are close enough of the solution, the problem
become locally convex.

To achieve this, we must contraction the simplex till it becomes valid.

Is it possible to tune the simplex algorithm to solve also those
locally convex problems.

Another problem is that the initial guest of the simplex is not always
possible. Can I create by myself the starting points of the simplex ?

 Frederic