Symmetric cone

Jordan automorphisms and derivatives of symmetric cones

  • Michael Orlitzky
    • Categories Cone Programming Tags , , , ,

    Hyperbolicity cones, and in particular symmetric cones, are of great interest in optimization. Renegar showed that every hyperbolicity cone has a family of derivative cones that approximate it. Ito and Lourenço found the automorphisms of those derivatives when the original cone is generated by rank-one elements, as symmetric cones happen to be. We show that … 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