Publication: A Conic Decompositions Approach for Semidefinite Programming

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Title A Conic Decompositions Approach for Semidefinite Programming
Authors/Editors* K. Krishnan, G. Plaza and T. Terlaky
Where published* AdvOl technical report series
How published* Technical Report
Year* 2005
Pages 54
Keywords conic linear optimization, decomposition mehods
We describe a conic interior point decomposition approach for solving large scale semidefinite programs (SDP) whose primal feasible sets are bounded. The idea is to solve such an SDP using existing primal-dual interior point methods, in an iterative fashion between a master problem and a set of subproblems. In our case, the master problem is a mixed conic problem over linear and smaller sized semidefinite cones. The subproblems are smaller semidefinite programs that either return a column or a small sized matrix depending on the multiplicity of the minimum eigenvalue of the dual slack matrix associated with this block. We motivate and develop the conic decomposition scheme and also discuss various issues involved in an efficient implementation. Computational results on several well known classes of semidefinite programs are presented.
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