Worst-Case Results For Positive Semidefinite Rank

This paper presents various worst-case results on the positive semidefinite (psd) rank of a nonnegative matrix, primarily in the context of polytopes. We prove that the psd rank of a generic n-dimensional polytope with v vertices is at least (nv)^(1/4) improving on previous lower bounds. For polygons with v vertices, we show that psd rank … Read more

Which Nonnegative Matrices Are Slack Matrices?

In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verifi cation problem whose complexity is unknown. Citation April 2013 Article Download View Which Nonnegative Matrices … Read more

Polytopes of Minimum Positive Semidefinite Rank

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, … Read more