- Polytopes of Minimum Positive Semidefinite Rank João Gouveia(jgouveiamat.uc.pt) Richard Z. Robinson(rzruw.edu) Rekha R. Thomas(rrthomasuw.edu) Abstract: The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound. Keywords: semidefinite programing, extended formulations, polytopes, nonnegative rank, semidefinite rank Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 2: Combinatorial Optimization (Polyhedra ) Citation: Download: [PDF]Entry Submitted: 05/29/2012Entry Accepted: 05/29/2012Entry Last Modified: 05/29/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.