Hi.
If I understood correctly, right now you are able to compute the values across a vector field as some mathematical function, and you want to automatically compute some local minimum depending on the parameters given (i.e., starting point on the vector field or surface). So I think you require to apply some optimization technique. I can help you with both Fortran and the optimization technique. Please, you can let me know more details (and also your deadline), and I can edit my bid accordingly.
You can check my freelance profile that I have been well evaluated in all my previous projects here (including recently, Fortran projects).
Thanks.