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Facial Reduction for Symmetry Reduced Semidefinite Programs

Hao Hu(h92hu***at***uwaterloo.ca)
Renata Sotirov(r.sotirov***at***uvt.nl)
Henry Wolkowicz(hwolkowi***at***uwaterloo.ca)

Abstract: We consider both facial and symmetry reduction techniques for semidefinite programming, SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers, ADMM, approach. The combination of facial and symmetry reduction leads to a significant improvement in both numerical stability and running time for both the ADMM and interior point approaches. We test our method on various doubly nonnegative, DNN, relaxations of hard combinatorial problems including quadratic assignment problems with sizes of more than $n=500$.

Keywords: Semidefinite programming, group symmetry, facial reduction, quadratic assignment problem, vertex separator problem

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 12/21/2019
Entry Accepted: 12/22/2019
Entry Last Modified: 12/21/2019

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