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From seven to eleven: completely positive matrices with high cp-rank

Immanuel Bomze (immanuel.bomze***at***univie.ac.at)
Werner Schachinger (werner.schachinger***at***univie.ac.at)
Reinhard Ullrich (reinhard.ullrich***at***univie.ac.at)

Abstract: We study $n\times n$ completely positive matrices $M$ on the boundary of the completely positive cone, namely those orthogonal to a copositive matrix $S$ which generates a quadratic form with finitely many zeroes in the standard simplex. Constructing particular instances of $S$, we are able to construct counterexamples to the famous Drew-Johnson-Loewy conjecture (1994) for matrices of order seven through eleven.

Keywords: copositive optimization, completely positive matrices, cp-rank, nonnegative factorization, circular symmetry

Category 1: Linear, Cone and Semidefinite Programming (Other )

Citation: Preprint NI14007-POP, Isaac Newton Institute for Mathematical Sciences, University of Cambridge UK, accepted for publication in: Linear Alg. Appl.

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Entry Submitted: 01/17/2014
Entry Accepted: 01/17/2014
Entry Last Modified: 06/19/2014

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