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Finding sparse, equivalent SDPs using minimal coordinate projections

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 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.
Date issued
2015-12
URI
https://hdl.handle.net/1721.1/121539
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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
ISBN
9781479978861

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