Approximating the maximum of a polynomial over a polytope: Handelman decomposition and continuous generating functions

Abstract

We investigate a way to approximate the maximum of a polynomial f over a polytopal region P through the computation of the integrals P f (x) k dx. We do a refined analysis of the quality of approximation for the resulting upper and lower bounds. We also propose a new methodology to compute those integrals using a Handelman polynomial decomposition and continuous multivariate generating functions.