homogeneous

On the non-homogeneity of completely positive cones

  • M. Seetharama Gowda
  • Roman Sznajder
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    Given a closed cone C in the Euclidean n-space, the completely positive cone of C is the convex cone K generated by matrices of the form uu^T as u varies over C. Examples of completely positive cones include the positive semidefinite cone (when C is the entire Euclidean n-space) and the cone of completely positive … Read more

    Recursive Construction of Optimal Self-Concordant Barriers for Homogeneous Cones

  • Olena Shevchenko
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper, we give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Guler and Tuncel by means of the dual Siegel cone construction of Rothaus. We use invariance of the primal barrier function with respect to a transitive subgroup … Read more