Integer Polynomial Optimization in Fixed Dimension
Abstract
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.
Cite
@article{arxiv.math/0410111,
title = {Integer Polynomial Optimization in Fixed Dimension},
author = {Jesús A. De Loera and Raymond Hemmecke and Matthias Köppe and Robert Weismantel},
journal= {arXiv preprint arXiv:math/0410111},
year = {2017}
}
Comments
In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully polynomial-time approximation scheme) to maximize a non-negative integer polynomial over the lattice points of a polytope