- On the computation of $C^*$ certificates Florian Jarre (jarreopt.uni-duesseldorf.de) Katrin Schmallowsky (schmallowskyopt.uni-duesseldorf.de) Abstract: The cone of completely positive matrices $C^*$ is the convex hull of all symmetric rank-1-matrices $xx^T$ with nonnegative entries. Determining whether a given matrix $B$ is completely positive is an $\cal NP$-complete problem. We examine a simple algorithm which -- for a given input $B$ -- either determines a certificate proving that $B\in C^*$ or converges to a matrix $\bar S$ in $C^*$ which in some sense is close'' to $B$. Numerical experiments on matrices $B$ of dimension up to 200 conclude the presentation. Keywords: Completely positive matrices Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Linear, Cone and Semidefinite Programming (Other ) Citation: Report, Mathematisches Institut, Universit\"at D\"usseldorf (2008) http://www.opt.uni-duesseldorf.de/en/forschung-fs.html Download: Entry Submitted: 05/04/2008Entry Accepted: 05/05/2008Entry Last Modified: 12/09/2010Modify/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 Programming Society.