Minimization in Fortran, starting point

[fortran90]

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 of 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)?

 

[mikrom]

There are several methods:
Gradient Method

http://en.wikipedia.org/wiki/Gradient_descent

Quasi-Newton methods

http://en.wikipedia.org/wiki/Quasi-Newton_method

especially Broyden, BGFS and SR1

http://en.wikipedia.org/wiki/Broyden's_method

http://en.wikipedia.org/wiki/BFGS_method

http://en.wikipedia.org/wiki/SR1_formula

 

[salgerman]

try looking in these places:
[URL unfurl="true"]http://www.fortran.com/the-fortran-company-homepage/fortran-tools-libraries-and-application-software/[/url]
[URL unfurl="true"]http://people.sc.fsu.edu/~jburkardt/f_src/f_src.html[/url]