José Mario Martínez

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

    Inexact Restoration for Minimization with Inexact Evaluation both of the Objective Function and the Constraints

  • Luís Felipe Bueno
  • F. Larreal
  • José Mario Martínez
    • Categories Constrained Nonlinear Optimization Tags , ,

    In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration methodology was employed, in a different research, to handle minimization problems with inexact evaluation and simple constraints. These two methodologies are … 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

    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 Bound-constrained Optimization, 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

    Complexity and performance of an Augmented Lagrangian algorithm

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

    Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and … Read more

    Iteration and evaluation complexity for the minimization of functions whose computation is intrinsically inexact

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

    In many cases in which one wishes to minimize a complicated or expensive function, it is convenient to employ cheap approximations, at least when the current approximation to the solution is poor. Adequate strategies for deciding the accuracy desired at each stage of optimization are crucial for the global convergence and overall efficiency of the … Read more