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An Augmented Lagrangian Method for Equality Constrained Optimization with Rapid Infeasibility Detection Capabilities

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  • Paul Armand

    (Université de Limoges - Laboratoire XLIM)

  • Ngoc Nguyen Tran

    (Université de Limoges - Laboratoire XLIM)

Abstract

We present a primal-dual augmented Lagrangian method for solving an equality constrained minimization problem, which is able to rapidly detect infeasibility. The method is based on a modification of the algorithm proposed in Armand and Omheni (Optim Methods Softw 32(1):1–21, 2017). A new parameter is introduced to scale the objective function and, in case of infeasibility, to force the convergence of the iterates to an infeasible stationary point. It is shown, under mild assumptions, that whenever the algorithm converges to an infeasible stationary point, the rate of convergence is quadratic. This is a new convergence result for the class of augmented Lagrangian methods. The global convergence of the algorithm is also analyzed. It is also proved that, when the algorithm converges to a stationary point, the properties of the original algorithm are preserved. The numerical experiments show that our new approach is as good as the original one when the algorithm converges to a local minimum, but much more efficient in case of infeasibility.

Suggested Citation

  • Paul Armand & Ngoc Nguyen Tran, 2019. "An Augmented Lagrangian Method for Equality Constrained Optimization with Rapid Infeasibility Detection Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 197-215, April.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1401-7
    DOI: 10.1007/s10957-018-1401-7
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    References listed on IDEAS

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    1. Paul Armand & Joël Benoist & Riadh Omheni & Vincent Pateloup, 2014. "Study of a primal-dual algorithm for equality constrained minimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 405-433, December.
    2. M. Gonçalves & J. Melo & L. Prudente, 2015. "Augmented Lagrangian methods for nonlinear programming with possible infeasibility," Journal of Global Optimization, Springer, vol. 63(2), pages 297-318, October.
    3. 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.
    4. Paul Armand & Riadh Omheni, 2017. "A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 523-547, May.
    5. E. G. Birgin & L. F. Bueno & J. M. Martínez, 2016. "Sequential equality-constrained optimization for nonlinear programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 699-721, December.
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    Cited by:

    1. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.

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