cubic regularization methods

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

    On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Nonlinear Optimization Tags , , , ,

    We propose a new termination criteria suitable for potentially singular, zero or non-zero residual, least-squares problems, with which cubic regularization variants take at most $\mathcal{O}(\epsilon^{-3/2})$ residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below $\epsilon$; this is the best-known bound for potentially singular nonlinear least-squares problems. We then … Read more