[Help-gsl] Numerical Minimization in multidimensions without derivatives and constraints

[Philipp Basler]

Hello to all,

I am using gsl_multimin_fminimizer_nmsimplex2 to minimize a function V (
v1,v2,v3) in those 3 variables v1,v2,v3. The function itself has a few more
parameters but those are constant during an Minimizationsprocess.
Also I can not calculate any derivatives of this function.
Normally you could just use the nmsimplex2 method to minimize this but I
have a further constraint :
In the process of calculating V(v1,v2,v3) there are two 4x4 real and
symmetric Matrices from whom I need the Eigenvalues, those are calculated
numerically with the Eigen package. All entries of those both Matrices are
functions of v1,v2 and v3 and therefore the Eigenvalues are too.
Now my constraint: If any of those 8 Eigenvalues is negativ I need  to
discard this combination of v1,v2,v3 and it is not allowed to enter my
search for a minimum.

Is there a way to do this?

Cheers,
Philipp