2015
On the existence of 0/1 polytopes with high semidefinite extension complexity
Publication
Publication
Mathematical Programming , Volume 153  Issue 1 p. 179 199
In Rothvoß (Math Program 142(1–2):255–268, 2013) it was shown that
there exists a 0/1 polytope (a polytope whose vertices are in {0, 1}n) such that any
higherdimensional polytope projecting to it must have 2Ω(n) facets, i.e., its linear
extension complexity is exponential. The question whether there exists a 0/1 polytope
with high positive semidefinite 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 semidefinite cone of dimension
2Ω(n) and an affine space. Our proof relies on a new technique to rescale semidefinite
factorizations.
Additional Metadata  

Logistics (theme 3)  
Springer  
doi.org/10.1007/s101070140785x  
Mathematical Programming  
Organisation  Algorithms and Complexity 
Briët, J, Dadush, D.N, & Pokutta, S. (2015). On the existence of 0/1 polytopes with high semidefinite extension complexity. Mathematical Programming, 153(1), 179–199. doi:10.1007/s101070140785x
