- On the cp-rank and minimal cp factorizations of a completely positive matrix Naomi Shaked-Monderer (nomitechunix.technion.ac.il) Immanuel M. Bomze (immanuel.bomzeunivie.ac.at) Florian Jarre (jarreopt.uni-duesseldorf.de) Werner Schachinger (werner.schachingerunivie.ac.at) Abstract: We show that the maximal cp-rank of $n\times n$ completely positive matrices is attained at a positive-definite matrix on the boundary of the cone of $n\times n$ completely positive matrices, thus answering a long standing question. We also show that the maximal cp-rank of $5\times 5$ matrices equals six, which proves the famous Drew-Johnson-Loewy conjecture (1994) for matrices of this order. In addition we present a simple scheme for generating completely positive matrices of high cp-rank and investigate the structure of a minimal cp factorization. Keywords: Copositive optimization, nonnegative factorization Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: appeared in SIAM J. Matrix Analysis Appl., http://epubs.siam.org/doi/abs/10.1137/120885759 Download: Entry Submitted: 06/27/2012Entry Accepted: 06/27/2012Entry Last Modified: 05/07/2013Modify/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 Optimization Online is supported by the Mathematical Optmization Society.