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D-gap functions and descent techniques for solving equilibrium problems

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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.

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Acknowledgments

The authors wish to thank the two anonymous referees and the associate editor for the careful reviews and valuable comments, which helped them to improve the paper.

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  1. Dipartimento di Informatica, Università di Pisa, Largo B.Pontecorvo, 3, 56127 , Pisa, Italy

    Giancarlo Bigi & Mauro Passacantando

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  1. Giancarlo Bigi
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  2. Mauro Passacantando
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Correspondence to Giancarlo Bigi.

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Bigi, G., Passacantando, M. D-gap functions and descent techniques for solving equilibrium problems. J Glob Optim 62, 183–203 (2015). https://doi.org/10.1007/s10898-014-0223-x

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  • DOI: https://doi.org/10.1007/s10898-014-0223-x

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