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Finding Descriptions of Polytopes via Extended Formulations and Liftings

by Kaibel, V.; Loos, A..

Series: 2011-28, Preprints

90C10 Integer programming
52B12 Special polytopes (linear programming, centrally symmetric, etc.)

We describe a technique to obtain linear descriptions for polytopes from extended formulations. The simple idea is to first define a suitable lifting function and then to find linear constraints that are valid for the polytope and guarantee lifted points to be contained in the extension. We explain the technique at an example from the literature (matching polytopes), obtain new simple proofs of results on path-set polytopes and small-cliques polytopes, and finally exploit the technique in order to derive linear descriptions of orbisacks, which are special Knapsack polytopes arising in the context of symmetry breaking in integer programming problems.

Polytope, Combinatorial Optimization, Extended Formulation, Linear Description, Projection