Basis selection for SOS programs via facial reduction and polyhedral approximations
Author(s)Permenter, Frank Noble; Parrilo, Pablo A.
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We develop a monomial basis selection procedure for sum-of-squares (SOS) programs based on facial reduction. Using linear programming and polyhedral approximations, the proposed technique finds a face of the SOS cone containing the feasible set of a given SOS program. The identified face in turn identifies a set of monomials that can be used to convert the SOS program into a semidefinite program (SDP). The technique can be viewed as a generalization of standard parsing algorithms for monomial basis selection. As we illustrate with examples, the proposed method can lead to smaller SDPs that are simpler to solve.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the IEEE Conference on Decision and Control
Institute of Electrical and Electronics Engineers (IEEE)
Permenter, Frank and Pablo a. Parrilo. "Basis selection for SOS programs via facial reduction and polyhedral approximations." In Proceedings of the IEEE Conference on Decision and Control, 53rd (February 2015).
Author's final manuscript