Canonical dual approach to solving the maximum cut problem

Authors:
Zhenbo Wang;Shu-Cherng Fang;David Y. Gao;Wenxun Xing
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing, China;Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA;School of Science, Information Technology and Engineering, University of Ballarat, Ballarat, Australia;Department of Mathematical Sciences, Tsinghua University, Beijing, China
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

This paper presents a canonical dual approach for finding either an optimal or approximate solution to the maximum cut problem (MAX CUT). We show that, by introducing a linear perturbation term to the objective function, the maximum cut problem is perturbed to have a dual problem which is a concave maximization problem over a convex feasible domain under certain conditions. Consequently, some global optimality conditions are derived for finding an optimal or approximate solution. A gradient decent algorithm is proposed for this purpose and computational examples are provided to illustrate the proposed approach.