chordal sparsity

Linear optimization over homogeneous matrix cones

  • Levent Tunçel
  • Lieven Vandenberghe
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that are homogeneous and self-dual are called symmetric. The symmetric cones include the … Read more

    Exploiting Aggregate Sparsity in Second Order Cone Relaxations for Quadratic Constrained Quadratic Programming Problems

  • Heejune Sheen
  • Makoto Yamashita
    • Categories Quadratic Programming, Second-Order Cone Programming, Semi-definite Programming Tags , , , ,

    Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP by Fukuda et al. (2001) and second-order cone programming (SOCP) relaxation have been popular. In this paper, we exploit the aggregate sparsity of SOCP … Read more