Approximate cone factorizations and lifts of polytopes
Optimization and Control
2015-09-04 v2
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.
Keywords
Cite
@article{arxiv.1308.2162,
title = {Approximate cone factorizations and lifts of polytopes},
author = {João Gouveia and Pablo A. Parrilo and Rekha R. Thomas},
journal= {arXiv preprint arXiv:1308.2162},
year = {2015}
}