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Approximate cone factorizations and lifts of polytopes

Author(s)
Gouveia, Joao; Parrilo, Pablo A.; Thomas, Rekha R.
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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.
Date issued
2014-12
URI
http://hdl.handle.net/1721.1/100986
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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
ISSN
0025-5610
1436-4646

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