I have a multipole potential energy surface depending on 7 variables and I would like to determine the equilibrium position(minimum). The potential is on a sum-of-products of small functions so it is not easy to derivate.
I tried to determine the minimum by intervals but I did not get any satisfactory result. <potential formular>
Many numerical optimization packages can work without derivatives (or they have accompanying functions to create approximations of derivatives).
To look for a suitable package, you might start with the Neos server.