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Gap functions and penalization for solving equilibrium problems with nonlinear constraints

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  • Giancarlo Bigi

    ()

  • Mauro Passacantando

    ()

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    Abstract

    The paper deals with equilibrium problems (EPs) with nonlinear convex constraints. First, EP is reformulated as a global optimization problem introducing a class of gap functions, in which the feasible set of EP is replaced by a polyhedral approximation. Then, an algorithm is given for solving EP through a descent type procedure, which exploits also exact penalty functions, and its global convergence is proved. Finally, the algorithm is tested on a network oligopoly problem with nonlinear congestion constraints. Copyright Springer Science+Business Media, LLC 2012

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9481-z
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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: 323-346

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    Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:323-346

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

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    Related research

    Keywords: Equilibrium problems; Gap function; Exact penalization; Descent direction;

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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.
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    Cited by:
    1. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    2. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.

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