-

 

 

 




Optimization Online





 

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 )

Citation:

Download: [PDF]

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

Modify/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
Mathematical Optimization Society