Margherita Porcelli

Preconditioning issues in the numerical solution of nonlinear equations and nonlinear least squares

  • Stefania Bellavia
  • Margherita Porcelli
    • Categories Nonlinear Optimization Tags , ,

    Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in Newton- Krylov methods will be … Read more

    A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for ℓ1-regularized least-squares

  • Margherita Porcelli
  • Francesco Rinaldi
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. in signal/image processing and statistics. A standard tool for dealing with sparse recovery is the ℓ1-regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version … Read more

    New updates of incomplete LU factorizations and applications to large nonlinear systems

  • Stefania Bellavia
  • Benedetta Morini
  • Margherita Porcelli
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we address the problem of preconditioning sequences of large sparse nonsymmetric systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete LU (ILU) factorization for one matrix of the sequence and differ in the approximation of … Read more

    Updating the regularization parameter in the adaptive cubic regularization algorithm

  • Nicholas I. M. Gould
  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    The adaptive cubic regularization method [Cartis, Gould, Toint, 2009-2010] has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to the local Lipschitz constant of the objective’s Hessian. We present new … Read more

    On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds

  • Margherita Porcelli
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. … Read more

    TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities

  • Benedetta Morini
  • Margherita Porcelli
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares

    The Matlab implementation of a trust-region Gauss-Newton method for bound-constrained nonlinear least-squares problems is presented. The solver, called TRESNEI, is adequate for zero and small-residual problems and handles the solution of nonlinear systems of equalities and inequalities. The structure and the usage of the solver are described and an extensive numerical comparison with functions from … Read more