Bharath Kumar Rangarajan

Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric Cones

  • Bharath Kumar Rangarajan
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    We establish polynomial-time convergence of infeasible-interior-point methods for conic programs over symmetric cones using a wide neighborhood of the central path. The convergence is shown for a commutative family of search directions used in Schmieta and Alizadeh. These conic programs include linear and semidefinite programs. This extends the work of Rangarajan and Todd, which established … Read more

    Convergence of infeasible-interior-point methods for self-scaled conic programming

  • Bharath Kumar Rangarajan
  • Michael J. Todd
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We present results on global and polynomial-time convergence of infeasible-interior-point methods for self-scaled conic programming, which includes linear and semidefinite programming. First, we establish global convergence for an algorithm using a wide neighborhood. Next, we prove polynomial complexity for the algorithm with a slightly narrower neighborhood. Both neighborhoods are related to the wide (minus infinity) … Read more