From seven to eleven: completely positive matrices with high cp-rank
Immanuel Bomze (immanuel.bomzeunivie.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.
Entry Submitted: 01/17/2014
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