Ernesto G. Birgin

Smoothing l1-exact penalty method for intrinsically constrained Riemannian optimization problems

  • Ernesto G. Birgin
  • Orizon Pereira Ferreira
  • Gabriel Haeser
  • Nelson Maculan
  • Lennin Mallma Ramirez
  • Leandro Fonseca Prudente
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    This paper deals with the Constrained Riemannian Optimization (CRO) problem, which involves minimizing a function subject to equality and inequality constraints on Riemannian manifolds. The study aims to advance optimization theory in the Riemannian setting by presenting and analyzing a penalty-type method for solving CRO problems. The proposed approach is based on techniques that involve … Read more

    A general merit function-based global convergent framework for nonlinear optimization

  • Luís Felipe Bueno
  • Ernesto G. Birgin
  • Tiara Martini
  • Dimary Moreno López
  • Thadeu Senne
  • Thiago Siqueira Santos
    • Categories Nonlinear Optimization Tags , , , , ,

    In this paper, we revisit the convergence theory of the inexact restoration paradigm for non-linear optimization. The paper first identifies the basic elements of a globally convergent method based on merit functions. Then, the inexact restoration method that employs a two-phase iteration is introduced as a special case. A specific implementation is presented that is … Read more

    On the global convergence of a general class of augmented Lagrangian methods

  • Ernesto G. Birgin
  • Gabriel Haeser
  • Nelson Maculan
  • Lennin Mallma Ramirez
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In [E. G. Birgin, R. Castillo and J. M. Martínez, Computational Optimization and Applications 31, pp. 31-55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is … Read more

    Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems

  • Ernesto G. Birgin
  • Gabriel Haeser
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , ,

    At each iteration of the Safeguarded Augmented Lagrangian algorithm Algencan, a bound-constrained subproblem consisting of the minimization of the Powell-Hestenes-Rockafellar augmented Lagrangian function is considered, for which a minimizer with tolerance tending to zero is sought. More precisely, a point that satisfies a subproblem first-order necessary optimality condition with tolerance tending to zero is required. … Read more

    Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls

  • Ernesto G. Birgin
  • Lucas Fernandez
  • Gabriel Haeser
  • Antoine
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , ,

    The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more

    Accelerated derivative-free spectral residual method for nonlinear systems of equations

  • Ernesto G. Birgin
  • José Mario Martínez
  • John L. Gardenghi
  • Diaulas S. Marcondes
    • Categories Nonlinear Systems and Least-Squares Tags , , , , ,

    Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely … Read more

    Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients

  • Ernesto G. Birgin
  • José Mario Martínez
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the number of variables is big (for the standards of derivative-free optimization), two dimension-reduction procedures are introduced. … Read more

    Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations

  • Ernesto G. Birgin
  • José Mario Martínez
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently, these methods are attractive for solving large-scale nonlinear systems. However, the convergence of these algorithms may be slow in critical cases; therefore, acceleration procedures are welcome. … Read more

    On complexity and convergence of high-order coordinate descent algorithms

  • V. S. Amaral
  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • Diaulas S. Marcondes
    • Categories Nonlinear Optimization Tags , ,

    Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with … Read more

    Economic inexact restoration for derivative-free expensive function minimization and applications

  • Ernesto G. Birgin
  • Nataša Krejić
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , , ,

    The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- … Read more