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Interior point methods for equilibrium problems

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  • Nils Langenberg

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Abstract

In the present paper we discuss three methods for solving equilibrium-type fixed point problems. Concentrating on problems whose solutions possess some stability property, we establish convergence of these three proximal-like algorithms that promise a very high numerical tractability and efficiency. For example, due to the implemented application of zone coercive Bregman functions, all these methods allow to treat the generated subproblems as unconstrained and, partly, explicitly solvable ones. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
  • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:453-483
    DOI: 10.1007/s10589-011-9450-y
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    References listed on IDEAS

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    1. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    2. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    3. Nils Langenberg, 2010. "Pseudomonotone operators and the Bregman Proximal Point Algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 537-555, August.
    4. Flam, S.D., 1999. "Learning Equilibrium Play: a Myopic Approach," Norway; Department of Economics, University of Bergen 189, Department of Economics, University of Bergen.
    5. Jacek Krawczyk, 2007. "Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems," Computational Management Science, Springer, vol. 4(2), pages 183-204, April.
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