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Polytopes of Minimum Positive Semidefinite Rank

João Gouveia(jgouveia***at***mat.uc.pt)
Richard Z. Robinson(rzr***at***uw.edu)
Rekha R. Thomas(rrthomas***at***uw.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 )


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Entry Submitted: 05/29/2012
Entry Accepted: 05/29/2012
Entry Last Modified: 05/29/2012

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