- The extreme rays of the $6\times6$ copositive cone Andrei Afonin(afonin.adphystech.edu) Roland Hildebrand(roland.hildebranduniv-grenoble-alpes.fr) Peter J.C. Dickinson(peter.jc.dickinsongooglemail.com) Abstract: We provide a complete classification of the extreme rays of the $6 \times 6$ copositive cone ${\cal COP}^6$. We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix $A \in {\cal COP}^6$. To each such minimal zero support set we construct a stratified semi-algebraic manifold in the space of real symmetric $6 \times 6$ matrices ${\cal S}^6$, parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices $A \in {\cal COP}^6$ having this minimal zero support set. Each semi-algebraic stratum is characterized by the supports of the minimal zeros $u$ as well as the supports of the corresponding matrix-vector products $Au$. The analysis uses recently and newly developed methods that are applicable also to copositive matrices of arbitrary order. Keywords: copositive matrix, extreme ray, minimal zero, non-convex optimization Category 1: Linear, Cone and Semidefinite Programming (Other ) Category 2: Global Optimization (Theory ) Citation: Download: [PDF]Entry Submitted: 11/22/2019Entry Accepted: 11/22/2019Entry Last Modified: 11/22/2019Modify/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.