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Degeneracy in Maximal Clique Decomposition for Semidefinite Programs

Arvind Raghunathan(raghunathan***at***merl.com)
Andrew Knyazev(knyazev***at***merl.com)

Abstract: Exploiting sparsity in Semidefinite Programs (SDP) is critical to solving large-scale problems. The chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in SDPs. In this paper, we show that the maximal clique-based SDP decomposition is primal degenerate when the SDP has a low rank solution. We also derive conditions under which the multipliers in the maximal clique-based SDP formulation is not unique. Numerical experiments demonstrate that the SDP decomposition results in the schur-complement matrix of the Interior Point Method (IPM) having higher condition number than for the original SDP formulation.

Keywords: semidefinite programming, primal degeneracy, dual multiplicity, ill-conditioning, IPM

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

Category 2: Convex and Nonsmooth Optimization

Citation: arXiv:1509.08021v1 (http://arxiv.org/abs/1509.08021)

Download: [PDF]

Entry Submitted: 09/28/2015
Entry Accepted: 09/28/2015
Entry Last Modified: 09/28/2015

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