Mitsuhiro Nishijima

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

    Generalizations of doubly nonnegative cones and their comparison

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

    In this study, we theoretically and numerically compare several generalizations of the doubly nonnegative (DNN) cone, which is frequently used to provide a relaxation that is tighter than that of the positive semidefinite cone for completely positive programming (CPP). To provide tighter relaxation for generalized CPP (GCPP) than the positive semidefinite cone, we generalize the … Read more