second-order conic optimization

Hadamard Directional Diff erentiability of the Optimal Value of a Linear Second-order Conic Programming Problem

  • Duan Qingsong
  • Liwei Zhang
  • Sainan Zhang
    • Categories Second-Order Cone Programming, Stochastic Programming Tags , , ,

    In this paper, we consider perturbation properties of a linear second-order conic optimization problem and its Lagrange dual in which all parameters in the problem are perturbed. We prove the upper semi-continuity of solution mappings for the primal problem and the Lagrange dual problem. We demonstrate that the optimal value function can be expressed as … Read more

    A New Primal-Dual Interior-Point Algorithm for Second-Order Cone Optimization

  • Yanqin Bai
  • Cornelis Roos
  • G. Q. Wang
    • Categories Linear, Cone and Semidefinite Programming, Second-Order Cone Programming Tags , , , ,

    We present a primal-dual interior-point algorithm for second-order conic optimization problems based on a specific class of kernel functions. This class has been investigated earlier for the case of linear optimization problems. In this paper we derive the complexity bounds $O(\sqrt{N})(\log N)\log\frac{N}{\epsilon})$ for large- and $O(\sqrt{N})\log\frac{N}{\epsilon}$ for small- update methods, respectively. Here $N$ denotes the … Read more