On the existence of 0/1 polytopes with high semidefinite extension complexity

  title={On the existence of 0/1 polytopes with high semidefinite extension complexity},
  author={Jop Bri{\"e}t and Daniel Dadush and Sebastian Pokutta},
  journal={Math. Program.},
In Rothvoß [2012] it was shown that there exists a 0/1 polytope (a polytope whose vertices are in {0, 1}) such that any higherdimensional polytope projecting to it must have 2 facets, i.e., its linear extension complexity is exponential. The question whether there exists a 0/1 polytope with high PSD extension complexity was left open. We answer this question in the affirmative by showing that there is a 0/1 polytope such that any spectrahedron projecting to it must be the intersection of a… CONTINUE READING
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