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Augmented Lagrangian and exact penalty methods for quasi-variational inequalities

Author

Listed:
  • Christian Kanzow

    (University of Würzburg)

  • Daniel Steck

    (University of Würzburg)

Abstract

A variant of the classical augmented Lagrangian method was recently proposed in Kanzow (Math Program 160(1–2, Ser. A):33–63, 2016), Pang and Fukushima (Comput Manag Sci 2(1):21–56, 2005) for the solution of quasi-variational inequalities (QVIs). In this paper, we describe an improved convergence analysis to the method. In particular, we introduce a secondary QVI as a new optimality concept for quasi-variational inequalities and use this tool to prove convergence theorems for certain popular classes of QVIs under very mild assumptions. Finally, we present a modification of the augmented Lagrangian method which turns out to be an exact penalty method, and also give detailed numerical results illustrating the performance of both methods.

Suggested Citation

  • Christian Kanzow & Daniel Steck, 2018. "Augmented Lagrangian and exact penalty methods for quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 69(3), pages 801-824, April.
  • Handle: RePEc:spr:coopap:v:69:y:2018:i:3:d:10.1007_s10589-017-9963-0
    DOI: 10.1007/s10589-017-9963-0
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    Cited by:

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    3. Axel Dreves & Simone Sagratella, 2020. "Nonsingularity and Stationarity Results for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 711-743, June.

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