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An Augmented Lagrangian method for quasi-equilibrium problems

Author

Listed:
  • L. F. Bueno

    (Federal University of São Paulo)

  • G. Haeser

    (University of São Paulo)

  • F. Lara

    (Universidad de Tarapacá)

  • F. N. Rojas

    (University of São Paulo)

Abstract

In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global convergence under a new weak constraint qualification, we extend the notion of an Approximate Karush–Kuhn–Tucker (AKKT) point for QEPs (AKKT-QEP), showing that in general it is not necessarily satisfied at a solution, differently from its counterpart in optimization. We study some particular cases where AKKT-QEP does hold at a solution, while discussing the solvability of the subproblems of the algorithm. We also present illustrative numerical experiments.

Suggested Citation

  • L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:3:d:10.1007_s10589-020-00180-4
    DOI: 10.1007/s10589-020-00180-4
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    References listed on IDEAS

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    Cited by:

    1. Ernesto G. Birgin, 2020. "Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 615-619, July.
    2. R. Andreani & E. H. Fukuda & G. Haeser & D. O. Santos & L. D. Secchin, 2021. "On the use of Jordan Algebras for improving global convergence of an Augmented Lagrangian method in nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 79(3), pages 633-648, July.

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