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arXiv · 1509.08021

Degeneracy in Maximal Clique Decomposition for Semidefinite Programs

Arvind U. Raghunathan·Andrew V. Knyazev
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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.

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Arvind U. Raghunathan, Andrew V. Knyazev. 2016-03-15. Degeneracy in Maximal Clique Decomposition for Semidefinite Programs. https://doi.org/10.1109/acc.2016.7526549

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