Tropical lower bounds for extended formulations

  title={Tropical lower bounds for extended formulations},
  author={Yaroslav Shitov},
  journal={Mathematical Programming},
  • Y. Shitov
  • Published 1 October 2015
  • Mathematics
  • Mathematical Programming
The tropical arithmetic operations on $$\mathbb {R}$$R, defined as $$\oplus :(a,b)\rightarrow \min \{a,b\}$$⊕:(a,b)→min{a,b} and $$\otimes :(a,b)\rightarrow a+b$$⊗:(a,b)→a+b, 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… 

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