M. Gokhan Ozevin

Convergence Analysis of a Weighted Barrier Decomposition Algorithm for Two Stage Stochastic Programming

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , ,

    Mehrotra and Ozevin computationally found that a weighted primal barrier decomposition algorithm significantly outperforms the barrier decomposition proposed and analyzed in Zhao, and Mehrotra and Ozevin. This paper provides a theoretical foundation for the weighted barrier decomposition algorithm (WBDA). Although the worst case analysis of the WBDA achieves a first-stage iteration complexity bound that is … Read more

    On the Implementation of Interior Point Decomposition Algorithms for Two-Stage Stochastic Conic

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Finance and Economics, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more

    Two-Stage Stochastic Semidefinite Programming and Decomposition Based Interior Point Methods

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Semi-definite Programming, Stochastic Programming Tags , , ,

    We introduce two-stage stochastic semidefinite programs with recourse and present a Benders decomposition based linearly convergent interior point algorithms to solve them. This extends the results of Zhao, who showed that the logarithmic barrier associated with the recourse function of two-stage stochastic linear programs with recourse behaves as a strongly self-concordant barrier on the first … Read more

    Analysis of a Path Following Method for Nonsmooth Convex Programs

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Convex and Nonsmooth Optimization Tags

    Recently Gilbert, Gonzaga and Karas [2001] constructed examples of ill-behaved central paths for convex programs. In this paper we show that under mild conditions the central path has sufficient smoothness to allow construction of a path-following interior point algorithm for non-differentiable convex programs. We show that starting from a point near the center of the … Read more