minimal zero

On the algebraic structure of the copositive cone

  • Roland Hildebrand
    • Categories Applications - OR and Management Sciences, Global Optimization Theory Tags , , ,

    We decompose the copositive cone $\copos{n}$ into a disjoint union of a finite number of open subsets $S_{\cal E}$ of algebraic sets $Z_{\cal E}$. Each set $S_{\cal E}$ consists of interiors of faces of $\copos{n}$. On each irreducible component of $Z_{\cal E}$ these faces generically have the same dimension. Each algebraic set $Z_{\cal E}$ is … Read more

    The extreme rays of the \times6$ copositive cone

  • Andrei Afonin
  • Peter J.C. Dickinson
  • Roland Hildebrand
    • Categories Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags , , ,

    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 … Read more