Symmetric cone

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 , , , , ,

    Our objective was to generalize the well-known doubly nonnegative (DNN) cone, and compare it with a generalized cone proposed by Burer and Dong in 2012. Several inner-approximation hierarchies for the generalized copositive cone over a closed cone have been proposed as generalizations of that proposed by Parrilo in 2000. By exploiting these hierarchies, we generalized … Read more