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Improved error bound and a hybrid method for generalized Nash equilibrium problems

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Abstract

We exploit a recently proposed local error bound condition for a nonsmooth reformulation of the Karush–Kuhn–Tucker conditions of generalized Nash equilibrium problems (GNEPs) to weaken the theoretical convergence assumptions of a hybrid method for GNEPs that uses a smooth reformulation. Under the presented assumptions the hybrid method, which combines a potential reduction algorithm and an LP-Newton method, has global and fast local convergence properties. Furthermore we adapt the algorithm to a nonsmooth reformulation, prove under some additional strong assumptions similar convergence properties as for the smooth reformulation, and compare the two approaches.

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Acknowledgments

We would like to thank the anonymous referees for their helpful comments.

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  1. Department of Aerospace Engineering, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Axel Dreves

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  1. Axel Dreves
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Correspondence to Axel Dreves.

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Dreves, A. Improved error bound and a hybrid method for generalized Nash equilibrium problems. Comput Optim Appl 65, 431–448 (2016). https://doi.org/10.1007/s10589-014-9699-z

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  • DOI: https://doi.org/10.1007/s10589-014-9699-z

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