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Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function

Author

Listed:
  • Nélida Echebest

    (University of La Plata)

  • María Daniela Sánchez

    (University of La Plata)

  • María Laura Schuverdt

    (University of La Plata)

Abstract

In the present research, an Augmented Lagrangian method with the use of the exponential penalty function for solving inequality constraints problems is considered. Global convergence is proved using the constant positive generator constraint qualification when the subproblem is solved in an approximate form. Since this constraint qualification was defined recently, the present convergence result is new for the Augmented Lagrangian method based on the exponential penalty function. Boundedness of the penalty parameters is proved considering classical conditions. Three illustrative examples are presented.

Suggested Citation

  • Nélida Echebest & María Daniela Sánchez & María Laura Schuverdt, 2016. "Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 92-108, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0735-7
    DOI: 10.1007/s10957-015-0735-7
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    References listed on IDEAS

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    1. H. Luo & X. Sun & Y. Xu & H. Wu, 2010. "On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints," Journal of Global Optimization, Springer, vol. 46(2), pages 217-232, February.
    2. E. Birgin & J. Martínez & L. Prudente, 2014. "Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming," Journal of Global Optimization, Springer, vol. 58(2), pages 207-242, February.
    3. H. Z. Luo & X. L. Sun & Y. F. Xu, 2010. "Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 489-506, June.
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