Completely positive cones

Copositive and completely positive cones over symmetric cones of rank at least 5

  • Mitsuhiro Nishijima
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We study copositive and completely positive cones over symmetric cones of rank at least $5$, with particular emphasis on whether these cones are spectrahedral shadows and on the behavior of a sum-of-squares inner-approximation hierarchy. We examine to what extent known results for nonnegative orthants of dimension at least $5$ carry over to general symmetric cones … Read more

    Facial structure of copositive and completely positive cones over a second-order cone

  • Mitsuhiro Nishijima
  • Bruno F. Lourenço
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , , , ,

    We classify the faces of copositive and completely positive cones over a second-order cone and investigate their dimension and exposedness properties. Then we compute two parameters related to chains of faces of both cones. At the end, we discuss some possible extensions of the results with a view toward analyzing the facial structure of general … Read more