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Regular version of the site

Article

Tropical lower bounds for extended formulations

Mathematical Programming. 2015. Vol. 153. No. 1. P. 67-74.

The tropical arithmetic operations on R arise from studying the geometry over non-Archimedean fields. We present an application of tropical methods to the study of extended formulations for convex polytopes. We propose a non-Archimedean generalization of the well known Boolean rank bound for the extension complexity. We show how to construct a real polytope with the same extension complexity and combinatorial type as a given non-Archimedean polytope. Our results allow us to develop a method of constructing real polytopes with large extension complexity.