固定维数下的整数多项式优化
最优化与控制
2017-01-03 v2 组合数学
摘要
我们依据计算复杂性对约束与目标函数均为整系数多项式且变量数固定的整数优化问题进行分类。对于在凸多面体格点上优化整数多项式的问题，我们给出计算最优值下界与上界的算法。对于在多面体上非负的多项式，这些界序列导出该优化问题的完全多项式时间近似格式。
引用
@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}
}
备注
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