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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

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    File URL: http://hdl.handle.net/10.1007/s10589-011-9450-y
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    Bibliographic Info

    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 53 (2012)
    Issue (Month): 2 (October)
    Pages: 453-483

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:453-483

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    Web page: http://www.springer.com/math/journal/10589

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    Related research

    Keywords: Equilibrium problems; Fixed point problems; Bregman distances; Proximal-like methods; Interior point effect;

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    1. Flam, S.D., 1999. "Learning Equilibrium Play: a Myopic Approach," Norway; Department of Economics, University of Bergen 189, Department of Economics, University of Bergen.
    2. Nils Langenberg, 2010. "Pseudomonotone operators and the Bregman Proximal Point Algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 537-555, August.
    3. Jacek B. Krawczyk & Steffan Berridge, 1997. "Relaxation Algorithms in Finding Nash Equilibria," Computational Economics 9707002, EconWPA.
    4. 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.
    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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