Ernesto G. Birgin

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

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

    At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, … Read more

    Continuous GRASP with a local active-set method for bound-constrained global optimization

  • Ernesto G. Birgin
  • Mauricio G.C. Resende
  • Ricardo M. A. Silva
  • Erico M. Gozzi
    • Categories Global Optimization, Stochastic Approaches Tags , , , , ,

    Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic – based on the CGRASP and GENCAN methods – for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN … Read more

    Global minimization using an Augmented Lagrangian method with variable lower-level constraints

  • Ernesto G. Birgin
  • Christodoulos A. Floudas
  • José Mario Martínez
    • Categories Global Optimization Tags , , ,

    A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration the method requires the $\varepsilon$-global minimization of the Augmented Lagrangian with simple constraints. Global convergence to an $\varepsilon$-global minimizer of the original problem is proved. The subproblems are solved using the $\alpha$BB … Read more

    On Augmented Lagrangian methods with general lower-level constraints

  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • María Laura Schuverdt
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lower-level type. Two methods of this class are introduced and analyzed. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved … Read more

    Augmented Lagrangian methods under the Constant Positive Linear Dependence constraint qualification

  • Roberto Andreani
  • Ernesto G. Birgin
  • José Mario Martínez
  • María Laura Schuverdt
    • Categories Nonlinear Optimization Tags , , ,

    Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under … Read more