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Which Nonnegative Matrices Are Slack Matrices?

J. Gouveia(jgouveia***at***mat.uc.pt)
R. Grappe(roland.grappe***at***gmail.com)
V. Kaibel(kaibel***at***ovgu.de)
K. Pashkovich(kanstantsin.pashkovich***at***gmail.com)
R. Z. Robinson(rzr***at***uw.edu)
R. R. Thomas(rrthomas***at***uw.edu)

Abstract: 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.

Keywords: slack matrices, polytopes, extended formulations, polyhedral verification problem

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: April 2013

Download: [PDF]

Entry Submitted: 03/31/2013
Entry Accepted: 04/01/2013
Entry Last Modified: 03/31/2013

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