MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

Timotej Hrga () and Janez Povh ()
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Timotej Hrga: University of Ljubljana
Janez Povh: University of Ljubljana

Computational Optimization and Applications, 2021, vol. 80, issue 2, No 2, 347-375

Abstract: Abstract We present MADAM, a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.

Keywords: Semidefinite programming; Alternating direction method of multipliers; Maximum cut problem; Parallel computing (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-021-00310-6

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