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arXiv · 1308.2162

Approximate cone factorizations and lifts of polytopes

João Gouveia·Pablo A. Parrilo·Rekha R. Thomas
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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.

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João Gouveia, Pablo A. Parrilo, Rekha R. Thomas. 2014-11-25. Approximate cone factorizations and lifts of polytopes. https://doi.org/10.1007/s10107-014-0848-z

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