polynomial convergence

An Iterative Solver-Based Long-Step Infeasible Primal-Dual Path-Following Algorithm for Convex QP Based on a Class of Preconditioners

  • Zhaosong Lu
  • Renato D.C. Monteiro
  • Jerome W. O'Neal
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , ,

    In this paper we present a long-step infeasible primal-dual path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of a preconditioned iterative linear solver. In contrast to the authors’ previous paper \cite{ONE04}, we propose a new linear system, which we refer to as the \emph{hybrid augmented normal equation} (HANE), to … Read more

    An Iterative Solver-Based Infeasible Primal-Dual Path-Following Algorithm for Convex QP

  • Zhaosong Lu
  • Renato D.C. Monteiro
  • Jerome W. O'Neal
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , ,

    In this paper we develop an interior-point primal-dual long-step path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of an iterative (linear system) solver. We propose a new linear system, which we refer to as the \emph{augmented normal equation} (ANE), to determine the primal-dual search directions. Since the condition number … Read more

    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

    Polynomial interior point cutting plane methods

  • John E. Mitchell
    • Categories Cutting Plane Approaches, Linear Programming, Nonsmooth Optimization Tags , , ,

    Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programming relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints should be added to the … Read more