V. S. Amaral

A flexible block coordinate descent method for unconstrained optimization under Hölder continuity

  • V. S. Amaral
  • Roberto Andreani
  • Leonardo D. Secchin
  • Gilson Silva
    • Categories Nonlinear Optimization, Unconstrained Optimization

    In this work, we propose a flexible block coordinate method for unconstrained optimization problems under Hölder continuity assumptions. The method guarantees convergence to stationary points and has worst-case complexity results comparable to those obtained by single-block methods that assume Lipschitz or Hölder continuity. The approach is based on quadratic models of the objective function combined … 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

    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