Extended formulations for radial cones

Matthias Walter; Stefan Weltge

doi:10.1016/j.orl.2019.05.004

Extended formulations for radial cones

Matthias Walter^*, Stefan Weltge

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

This paper studies extended formulations for radial cones at vertices of polyhedra, which are the polyhedra defined by the constraints that are active at the vertex. While the perfect-matching polytope cannot be described by subexponential-size extended formulations (Rothvoß 2014), Ventura & Eisenbrand (2003) showed that its radial cones can be described by polynomial-size extended formulations. The authors also asked whether this extends to odd-cut polyhedra, which are related to matching polyhedra by polarity. We answer this question negatively.

Original language	English
Pages (from-to)	458-463
Number of pages	6
Journal	Operations research letters
Volume	47
Issue number	5
Early online date	4 Jun 2019
DOIs	https://doi.org/10.1016/j.orl.2019.05.004
Publication status	Published - 1 Sept 2019

Keywords

Extension complexity
Matching polytope
Odd-cut polyhedron
Radial cones

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abstract = "This paper studies extended formulations for radial cones at vertices of polyhedra, which are the polyhedra defined by the constraints that are active at the vertex. While the perfect-matching polytope cannot be described by subexponential-size extended formulations (Rothvo{\ss} 2014), Ventura & Eisenbrand (2003) showed that its radial cones can be described by polynomial-size extended formulations. The authors also asked whether this extends to odd-cut polyhedra, which are related to matching polyhedra by polarity. We answer this question negatively.",

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AB - This paper studies extended formulations for radial cones at vertices of polyhedra, which are the polyhedra defined by the constraints that are active at the vertex. While the perfect-matching polytope cannot be described by subexponential-size extended formulations (Rothvoß 2014), Ventura & Eisenbrand (2003) showed that its radial cones can be described by polynomial-size extended formulations. The authors also asked whether this extends to odd-cut polyhedra, which are related to matching polyhedra by polarity. We answer this question negatively.

KW - Extension complexity

KW - Matching polytope

KW - Odd-cut polyhedron

KW - Radial cones

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JO - Operations research letters

JF - Operations research letters

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ER -

Extended formulations for radial cones

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Keywords

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