FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension
Optimization and Control
2017-01-03 v1
Abstract
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed.
Cite
@article{arxiv.0706.2354,
title = {FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension},
author = {Jesús A. De Loera and Raymond Hemmecke and Matthias Köppe and Robert Weismantel},
journal= {arXiv preprint arXiv:0706.2354},
year = {2017}
}