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D-gap functions and descent techniques for solving equilibrium problems

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  • Giancarlo Bigi
  • Mauro Passacantando

Abstract

A new algorithm for solving equilibrium problems with differentiable bifunctions is provided. The algorithm is based on descent directions of a suitable family of D-gap functions. Its convergence is proved under assumptions which do not guarantee the equivalence between the stationary points of the D-gap functions and the solutions of the equilibrium problem. Moreover, the algorithm does not require to set parameters according to thresholds which depend on regularity properties of the equilibrium bifunction. The results of preliminary numerical tests on Nash equilibrium problems with quadratic payoffs are reported. Finally, some numerical comparisons with other D-gap algorithms are drawn relying on some further tests on linear equilibrium problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:183-203
    DOI: 10.1007/s10898-014-0223-x
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    References listed on IDEAS

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    1. 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.
    2. N. Yamashita & K. Taji & M. Fukushima, 1997. "Unconstrained Optimization Reformulations of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 439-456, March.
    3. 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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    Cited by:

    1. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.

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