I am interested in finding minimizers of functionals of the type $\sum x^ay^bz^c$ where the exponents are 1, 0 or -1. I have codes to find such minimizers when they exist up to machine precision, using standard optimization ideas.
In view of some applications in probability theory, people are not satisfied with "precise results" but would rather like exact ones. I know that the problem above is what is called a "geometric programming problem", and there are specific algorithms to find the minimum. However, Matlab versions I've tried give still very precise, but approximate results.
Is it possible to build a symbolic version for such Geometric Programming algorithms? Do you know any works in this direction?