TY - JOUR

T1 - Approximation Algorithms for Discrete Polynomial Optimization

AU - He, Simai

AU - Li, Zhening

AU - Zhang, Shuzhong

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - Approximation algorithm

KW - Approximation ratio

KW - Binary integer programming

KW - Mixed integer programming

KW - Polynomial optimization problem

UR - http://www.scopus.com/inward/record.url?scp=84899078103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899078103&partnerID=8YFLogxK

U2 - 10.1007/s40305-013-0003-1

DO - 10.1007/s40305-013-0003-1

M3 - Article

AN - SCOPUS:84899078103

VL - 1

SP - 3

EP - 36

JO - Journal of the Operations Research Society of China

JF - Journal of the Operations Research Society of China

SN - 2194-668X

IS - 1

ER -