An efficient Lagrangian smoothing heuristic for Max-Cut

Yong Xia and Zi Xu ()
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Yong Xia: Beihang University
Zi Xu: Beihang University

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 5, 683-700

Abstract: Abstract Max-Cut is a famous NP-hard problem in combinatorial optimization. In this article, we propose a Lagrangian smoothing algorithm for Max-Cut, where the continuation subproblems are solved by the truncated Frank-Wolfe algorithm. We establish practical stopping criteria and prove that our algorithm finitely terminates at a KKT point, the distance between which and the neighbour optimal solution is also estimated. Additionally, we obtain a new sufficient optimality condition for Max-Cut. Numerical results indicate that our approach outperforms the existing smoothing algorithm in less time.

Keywords: Max-Cut; Lagrangian smoothing; Frank-Wolfe algorithm; heuristic (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0039-4

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