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A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application

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Abstract

We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on a local error bound and provide a new sufficient condition for it to hold that is weaker than known ones. In particular, this condition implies neither local uniqueness of a solution nor strict complementarity. We also report promising numerical results.

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Acknowledgements

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

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Authors and Affiliations

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

    Axel Dreves

  2. Department of Computer, Control, and Management Engineering Antonio Ruberti, University of Rome La Sapienza, Via Ariosto 25, 00185, Roma, Italy

    Francisco Facchinei

  3. Institute of Numerical Mathematics, Department of Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Andreas Fischer & Markus Herrich

Authors
  1. Axel Dreves
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  2. Francisco Facchinei
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  3. Andreas Fischer
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  4. Markus Herrich
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Corresponding author

Correspondence to Markus Herrich.

Additional information

This paper is dedicated to our colleague and friend Masao Fukushima on occasion of his 65th birthday, to honor his vast contribution to optimization.

This work is supported in a part by the German Research Foundation (DFG) in the Collaborative Research Center 912 “Highly Adaptive Energy-Efficient Computing”.

The paper was partially completed while the last three authors were visiting the Institute for Mathematical Sciences, National University of Singapore in 2012.

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Dreves, A., Facchinei, F., Fischer, A. et al. A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application. Comput Optim Appl 59, 63–84 (2014). https://doi.org/10.1007/s10589-013-9586-z

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