irreducible

Generating irreducible copositive matrices using the stable set problem

  • Reinier de Zeeuw
  • Peter J.C. Dickinson
    • Categories Convex Optimization, Graphs and Matroids, Linear, Cone and Semidefinite Programming Tags , , , ,

    In this paper it is considered how graphs can be used to generate copositive matrices, and necessary and sufficient conditions are given for these generated matrices to then be irreducible with respect to the set of positive semidefinite plus nonnegative matrices. This is done through combining the well known copositive formulation of the stable set … Read more

    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