Computational Optimization and Applications

, Volume 69, Issue 3, pp 801–824 | Cite as

Augmented Lagrangian and exact penalty methods for quasi-variational inequalities

  • Christian Kanzow
  • Daniel Steck


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.


Quasi-variational inequality Augmented Lagrangian method Global convergence Feasibility Exact penalty 


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Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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