Approximate cone factorizations and lifts of polytopes
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Parrilo_Approximate cone.pdf
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Author(s)
Gouveia, Joao
Parrilo, Pablo A.
Thomas, Rekha R.
Date Issued
December 2014
Journal
Mathematical Programming
Publisher
Springer-Verlag
Citation
Gouveia, Joao, Pablo A. Parrilo, and Rekha R. Thomas. “Approximate Cone Factorizations and Lifts of Polytopes.” Math. Program. 151, no. 2 (December 3, 2014): 613–637.
Version
Author's final manuscript
Abstract
In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave well under polarity and have efficient representations using second order cones. We establish a direct relationship between the quality of the factorization and the quality of the approximations, and our results extend to generalized slack matrices that arise from a polytope contained in a polyhedron.
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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DOI of Published Version
https://doi.org/10.1007/s10107-014-0848-z
