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arXiv · 1404.2752

Hidden Vertices in Extensions of Polytopes

Kanstantsin Pashkovich·Stefan Weltge
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Abstract

Some widely known compact extended formulations have the property that each vertex of the corresponding extension polytope is projected onto a vertex of the target polytope. In this paper, we prove that for heptagons with vertices in general position none of the minimum size extensions has this property. Additionally, for any d >= 2 we construct a family of d-polytopes such that at least 1/9 of all vertices of any of their minimum size extensions is not projected onto vertices.

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Kanstantsin Pashkovich, Stefan Weltge. 2015-01-11. Hidden Vertices in Extensions of Polytopes. https://arxiv.org/abs/1404.2752

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