Russell Luke

Nonexpansive Markov Operators and Random Function Iterations for Stochastic Fixed Point Problems

  • Russell Luke
    • Categories Global Optimization Theory, Stochastic Approaches, Stochastic Programming Tags , ,

    We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant mea- sure the stochastic fixed point problem. This generalizes earlier work studying the stochastic feasibility problem, namely, to find points that are, with probability 1, fixed points of … Read more

    Activity Identification and Local Linear Convergence of Douglas-Rachford/ADMM under Partial Smoothness

  • Jalal Fadili
  • Jingwei Liang
  • Russell Luke
  • Gabriel Peyré
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Proximal splitting algorithms are becoming popular to solve convex optimization problems in variational image processing. Within this class, Douglas-Rachford (DR) and ADMM are designed to minimize the sum of two proper lower semicontinuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of … Read more

    Local convergence for alternating and averaged nonconvex projections

  • Adrian Lewis
  • Jérôme Malick
  • Russell Luke
    • Categories Constrained Nonlinear Optimization, Control Applications, Nonsmooth Optimization Tags , , , , , , , ,

    The idea of a finite collection of closed sets having “strongly regular intersection” at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably “regular” (special cases being convex … Read more