Bruno F. Lourenço

Solving SDP Completely with an Interior Point Oracle

  • Bruno F. Lourenço
  • Masakazu Muramatsu
  • Takashi Tsuchiya
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , ,

    We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater’s condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general SDPs even after certain regularization schemes are applied. In this work we fill this gap and show … Read more

    A structural geometrical analysis of weakly infeasible SDPs

  • Bruno F. Lourenço
  • Masakazu Muramatsu
  • Takashi Tsuchiya
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags ,

    In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). We introduce the concept of hyper feasible partitions and sub-hyper feasible directions, and show how they can be used to decompose SDFPs into smaller ones, in a way that preserves most feasibility properties of the original problem. With this technique, we … Read more