Basis selection for SOS programs via facial reduction and polyhedral approximations
Name
fr_sos.pdf
Description
Accepted version
Size
283.69 KB
Format
Adobe PDF
Checksum (MD5)
0645e9aa014511ffe133e9fd13962dba
Author(s)
Permenter, Frank Noble
Parrilo, Pablo A.
Date Issued
February 2015
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
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/CDC.2014.7040427
