Copositive cone

On the longest chain of faces of completely positive and copositive cones

  • Mitsuhiro Nishijima
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming Tags , , , , ,

    We consider a wide class of closed convex cones K in the space of real n*n symmetric matrices and establish the existence of a chain of faces of K, the length of which is maximized at n(n+1)/2 + 1. Examples of such cones include, but are not limited to, the completely positive and the copositive … Read more

    Approximation hierarchies for copositive cone over symmetric cone and their comparison

  • Mitsuhiro Nishijima
  • Kazuhide Nakata
    • Categories Cone Programming, Convex Optimization, Global Optimization Theory Tags , , , ,

    We first provide an inner-approximation hierarchy described by a sum-of-squares (SOS) constraint for the copositive (COP) cone over a general symmetric cone. The hierarchy is a generalization of that proposed by Parrilo (2000) for the usual COP cone (over a nonnegative orthant). We also discuss its dual. Second, we characterize the COP cone over a … Read more