par Conforti, Michele;Pashkovich, Kanstantsin 
Référence Mathematical programming, 156, 1-2, page (331-342)
Publication Publié, 2016-03
Référence Mathematical programming, 156, 1-2, page (331-342)
Publication Publié, 2016-03
Article révisé par les pairs
| Résumé : | Margot (1994) in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from “smaller” polytopes via some composition rule. He introduced the “projected faces property” of a polytope and showed that this property suffices to iteratively build extended formulations of composed polytopes. For the composed polytopes, we show that an extended formulation of the type defined by Margot is always possible only if the smaller polytopes have the projected faces property. Therefore, this produces a characterization of the projected faces property. Affinely generated polyhedral relations were introduced by Kaibel and Pashkovich (Optima 85:2–7, 2011) to construct extended formulations for the convex hull of the images of a point under the action of some finite group of reflections. In this paper we prove that the projected faces property and affinely generated polyhedral relation are equivalent conditions. |
