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

TL;DR

This paper presents a polynomial-time approximation method for maximizing a polynomial over a polytope using Handelman's decomposition and generating functions, effective in fixed dimensions despite the NP-hardness of the problem.

Contribution

It introduces a novel approach combining Handelman's decomposition with generating functions to approximate polynomial maxima over polytopes efficiently.

Findings

Approximation method runs in polynomial time for fixed dimensions.

Effective for NP-hard polynomial maximization problems.

Combines algebraic and analytical techniques for optimization.

Abstract

We investigate a way to approximate the maximum of a polynomial over a polytopal region by using Handelman's polynomial decomposition and continuous multivariate generating functions. The maximization problem is NP-hard, but our approximation methods will run in polynomial time when the dimension is fixed.