Approximation algorithms for discrete polynomial optimization

Simai He, Zhening Li, Shuzhong Zhang

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Abstract

In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variables; (2) maximizing a homogeneous polynomial function in binary variables, mixed with variables under spherical constraints; (3) maximizing an inhomogeneous polynomial function in binary variables. We propose polynomial-time randomized approximation algorithms for such polynomial optimization models, and establish the approximation ratios (or relative approximation ratios whenever appropriate) for the proposed algorithms. Some examples of applications for these models and algorithms are discussed as well.
Original languageEnglish
Pages (from-to)3-36
JournalJournal of the Operations Research Society of China
Volume1
Issue number1
Early online date19 Feb 2013
DOIs
Publication statusPublished - Mar 2013

Keywords

  • polynomial optimization problem
  • binary integer programming
  • mixed integer programming
  • approximation algorithm
  • approximation ratio

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