homogeneous cone

Faces of homogeneous cones and applications to homogeneous chordality

  • João Gouveia
  • Masaru Ito
  • Bruno F. Lourenço
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    A convex cone K is said to be homogeneous if its group of automorphisms acts transitively on its relative interior. Important examples of homogeneous cones include symmetric cones and cones of positive semidefinite (PSD) matrices that follow a sparsity pattern given by a homogeneous chordal graph. Our goal in this paper is to elucidate the … 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