A semidefinite programming based polyhedral cut and price algorithm for the maxcut problem

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Kartik Krishnan
Harrelson Hall 235
Department of Mathematics
Campus Box 8205
North Carolina State University
Raleigh, NC 27695-8205 USA
kksivara at ncsu.edu

John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA

Computational Optimization and Applications, Volume 33(1), pages 51-71, 2006.


We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme.

Keywords: Semidefinite programming, column generation, cutting plane methods, combinatorial optimization.

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