predictor-corrector methods

A Homogeneous Predictor-Corrector Algorithm for Stochastic Nonsymmetric Convex Conic Optimization With Discrete Support

  • Baha Alzalg
  • Mohammad Alabedalhadi
    • Categories Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , ,

    We consider a stochastic convex optimization problem over nonsymmetric cones with discrete support. This class of optimization problems has not been studied yet. By using a logarithmically homogeneous self-concordant barrier function, we present a homogeneous predictor-corrector interior-point algorithm for solving stochastic nonsymmetric conic optimization problems. We also derive an iteration bound for the proposed algorithm. … Read more

    Local superlinear convergence of polynomial-time interior-point methods for hyperbolic cone optimization problems

  • Yurii Nesterov
  • Levent Tunçel
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier function, which must have {\em negative curvature}. We propose a new path-following predictor-corrector scheme, which work only … Read more

    Mehrotra-type predictor-corrector algorithms revisited

  • Maziar Salahi
  • Tamás Terlaky
    • Categories Linear Programming Tags , , , ,

    Motivated by a numerical example which shows that a feasible version of Mehrotra’s original predictor-corrector algorithm might be inefficient in practice, Salahi et al., proposed a so-called safeguard based variant of the algorithm that enjoys polynomial iteration complexity while its practical efficiency is preserved. In this paper we analyze the same Mehrotra’s algorithm from a … Read more