Numerical Minimization of many-variable function in Fortran

[dftfunctional]

I would like to find a FORTRAN subroutine or a good way to minimize function numerically.So basically my function has 20 variables and I am able to provide analytic form of the first and the second derivative of the function. Basically what I want is: have the form of the function of 20 variables, I assign values to e.g. 14 variables and to find the set of values for the rest variables in order to have the minimized value of the function. Any tips how to do this or where to search for subroutine (trying to avoid local minima)?

 

[DrClaude]

Finding the global minimum of a multi-dimensional function is an art! There are many methods, and which to choose depends a lot on the function.

You could use genetic algorithms or simulated annealing, for instance. For the latter case, a found Fortran source code that implements it:
http://ideas.repec.org/c/wpa/wuwppr/9406001.html

You can also have a look at http://arnold-neumaier.at/glopt/software_g.html