p-cone

The automorphism group and the non-self-duality of p-cones

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

    In this paper, we determine the automorphism group of the p-cones (p\neq 2) in dimension greater than two. In particular, we show that the automorphism group of those p-cones are the positive scalar multiples of the generalized permutation matrices that fix the main axis of the cone. Next, we take a look at a problem … Read more

    The p-cones in dimension n>=3 are not homogeneous when p \neq 2

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

    Using the T-algebra machinery we show that the only strictly convex homogeneous cones in R^n with n >= 3 are the 2-cones, also known as Lorentz cones or second order cones. In particular, this shows that the p-cones are not homogeneous when p is not 2, 1 < p <\infty and n >= 3, thus … Read more