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Gap functions and penalization for solving equilibrium problems with nonlinear constraints


  • Giancarlo Bigi


  • Mauro Passacantando



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

Suggested Citation

  • Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
  • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:323-346
    DOI: 10.1007/s10589-012-9481-z

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    References listed on IDEAS

    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. repec:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2013-3 is not listed on IDEAS
    3. Giancarlo Bigi & Mauro Passacantando, 2015. "D-gap functions and descent techniques for solving equilibrium problems," Journal of Global Optimization, Springer, vol. 62(1), pages 183-203, May.
    4. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    5. repec:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-016-0974-2 is not listed on IDEAS
    6. Gábor Kassay & Mihaela Miholca, 2015. "Existence results for vector equilibrium problems given by a sum of two functions," Journal of Global Optimization, Springer, vol. 63(1), pages 195-211, September.
    7. 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.
    8. repec:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0473-7 is not listed on IDEAS


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