Approximating the maximum of a polynomial over a polytope: Handelman decomposition and continuous generating functions
Optimization and Control
2016-06-28 v2
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.
Cite
@article{arxiv.1601.04118,
title = {Approximating the maximum of a polynomial over a polytope: Handelman decomposition and continuous generating functions},
author = {Jesús De Loera and Brandon Dutra and Matthias Köppe},
journal= {arXiv preprint arXiv:1601.04118},
year = {2016}
}
Comments
version 2: improved the main proof and expanded the Handelman theory