Finding sparse, equivalent SDPs using minimal coordinate projections
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invariant.pdf
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Accepted version
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280.91 KB
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Author(s)
Permenter, Frank Noble
Parrilo, Pablo A.
Date Issued
December 2015
Journal
2015 54th IEEE Conference on Decision and Control (CDC)
Publisher
IEEE
Citation
Permenter, Frank, and Pablo A. Parrilo. “Finding Sparse, Equivalent SDPs Using Minimal Coordinate Projections.” 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15-18 December 2015, IEEE, 2015, pp. 7274–79.
Version
Author's final manuscript
Abstract
We present a new method for simplifying SDPs that blends aspects of symmetry reduction with sparsity exploitation. By identifying a subspace of sparse matrices that provably intersects (but doesn't necessarily contain) the set of optimal solutions, we both block-diagonalize semidefinite constraints and enhance problem sparsity for many SDPs arising in sums-of-squares optimization. The identified subspace is in analogy with the fixed-point subspace that appears in symmetry reduction, and, as we illustrate, can be found using an efficient combinatorial algorithm that searches over coordinate projections. Effectiveness of the method is illustrated on several examples.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/cdc.2015.7403367
