Optimization Online


The extreme rays of the $6\times6$ copositive cone

Andrei Afonin(afonin.ad***at***phystech.edu)
Roland Hildebrand(roland.hildebrand***at***univ-grenoble-alpes.fr)
Peter J.C. Dickinson(peter.jc.dickinson***at***googlemail.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 )


Download: [PDF]

Entry Submitted: 11/22/2019
Entry Accepted: 11/22/2019
Entry Last Modified: 11/22/2019

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society