random models

A stochastic Levenberg-Marquardt method using random models with complexity results and application to data assimilation

  • Elhoucine Bergou
  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • ClĂ©ment W. Royer
    • Categories Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

    Globally convergent variants of the Gauss-Newton algorithm are often the methods of choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg-Marquardt and trust-region methods are two well-established, similar paradigms. Both schemes have been studied when the Gauss-Newton model is replaced by a random model that is only accurate with a given probability. Trust-region schemes … Read more

    Global convergence rate analysis of unconstrained optimization methods based on probabilistic models

  • Coralia Cartis
  • Katya Scheinberg
    • Categories Unconstrained Optimization Tags , , ,

    We present global convergence rates for a line-search method which is based on random first-order models and directions whose quality is ensured only with certain probability. We show that in terms of the order of the accuracy, the evaluation complexity of such a method is the same as its counterparts that use deterministic accurate models; … Read more

    Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation

  • Elhoucine Bergou
  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Systems and Least-Squares, Stochastic Programming Tags , , , , , , ,

    The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this paper the extension of the classical Levenberg-Marquardt algorithm to the scenarios where the linearized least squares subproblems are solved inexactly and/or the gradient model is … Read more