Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone
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Author(s)
Permenter, Frank Noble
Parrilo, Pablo A
Date Issued
June 2017
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Permenter, Frank, and Pablo Parrilo. “Partial Facial Reduction: Simplified, Equivalent SDPs via Approximations of the PSD Cone.” Mathematical Programming, vol. 171, no. 1–2, Sept. 2018, pp. 1–54.
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Author's final manuscript
Abstract
We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible solution (a frequent output of parsers) by solving a sequence of easier optimization problems and could be a useful pre-processing technique for SDP solvers. We demonstrate effectiveness of the method on SDPs arising in practice, and describe our publicly-available software implementation. We also show how to find maximum rank matrices in our PSD cone approximations (which helps us find maximal simplifications), and we give a post-processing procedure for dual solution recovery that generally applies to facial-reduction-based pre-processing techniques. Finally, we show how approximations can be chosen to preserve problem sparsity.
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/10.1007/s10107-017-1169-9
