second-order cone optimization

A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems, with Convergence Proofs

  • Dianne P. O'Leary
  • Sungwoo Park
    • Categories Semi-definite Programming Tags , , , , , , , , ,

    We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction … Read more

    A conic representation of the convex hull of disjunctive sets and conic cuts for integer second order cone optimization

  • Pietro Belotti
  • Julio C. Góez
  • Imre Pólik
  • Ted K. Ralphs
  • Tamás Terlaky
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming Tags , ,

    We study the convex hull of the intersection of a convex set E and a linear disjunction. This intersection is at the core of solution techniques for Mixed Integer Conic Optimization. We prove that if there exists a cone K (resp., a cylinder C) that has the same intersection with the boundary of the disjunction … Read more

    Full Nesterov-Todd Step Primal-Dual Interior-Point Methods for Second-Order Cone Optimization

  • G. Gu
  • Cornelis Roos
  • M. Zangiabadi
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    After a brief introduction to Jordan algebras, we present a primal-dual interior-point algorithm for second-order conic optimization that uses full Nesterov-Todd-steps; no line searches are required. The number of iterations of the algorithm is $O(\sqrt{N}\log ({N}/{\varepsilon})$, where $N$ stands for the number of second-order cones in the problem formulation and $\varepsilon$ is the desired accuracy. … Read more