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Decomposing the Algebra Associated to an SDP


P.A. Parrilo

Minneapolis, MN, USA, IMA Workshop on Semidefinite Programming and Robust Optimization. Institute for Mathematics and its Applications

We study the associative algebra corresponding to a given semidefinite program. We show how to explicitly decompose it as a direct sum of "smaller" algebras, greatly simplifying its numerical solution. The results are motivated by our earlier work with Karin Gatermann on symmetry reduction for SOS/SDP, and enable improved techniques for problems with large groups. The results will be illustrated through applications of sum of squares techniques in quantum mechanics.

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