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On the multiplier-penalty-approach for quasi-variational inequalities

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Abstract

The multiplier-penalty approach is one of the classical methods for the solution of constrained optimization problems. This method was generalized to the solution of quasi-variational inequalities by Pang and Fukushima (Comput Manag Sci 2:21–56, 2005). Based on the recent improvements achieved for the multiplier-penalty approach for optimization, we generalize the method by Pang and Fukushima for quasi-variational inequalities in several respects: (a) We allow to compute inexact KKT-points of the resulting subproblems; (b) We improve the existing convergence theory; (c) We investigate some special classes of quasi-variational inequalities where the resulting subproblems turn out to be easy to solve. Some numerical results indicate that the corresponding method works quite reliable in practice.

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Acknowledgments

The author would like to thank both referees for pointing out reference [1] and making several suggestions that helped to improve the presentation.

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  1. Institute of Mathematics, University of Würzburg, Emil-Fischer-Str. 30, 97074, Würzburg, Germany

    Christian Kanzow

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  1. Christian Kanzow
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Kanzow, C. On the multiplier-penalty-approach for quasi-variational inequalities. Math. Program. 160, 33–63 (2016). https://doi.org/10.1007/s10107-015-0973-3

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