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Basis selection for SOS programs via facial reduction and polyhedral approximations

Author(s)
Permenter, Frank Noble; Parrilo, Pablo A.
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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Abstract
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.
Date issued
2015-02
URI
https://hdl.handle.net/1721.1/121514
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
Proceedings of the IEEE Conference on Decision and Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
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).
Version: Author's final manuscript
ISSN
0191-2216

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