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.

Bigi, G., Passacantando, M. (2015). D-gap functions and descent techniques for solving equilibrium problems. JOURNAL OF GLOBAL OPTIMIZATION, 62(1), 183-203 [10.1007/s10898-014-0223-x].

D-gap functions and descent techniques for solving equilibrium problems

Passacantando, M
2015

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.
No
Articolo in rivista - Articolo scientifico
Scientifica
D-gap function; Descent directions; Equilibrium problem; Monotonicity
English
183
203
21
Bigi, G., Passacantando, M. (2015). D-gap functions and descent techniques for solving equilibrium problems. JOURNAL OF GLOBAL OPTIMIZATION, 62(1), 183-203 [10.1007/s10898-014-0223-x].
Bigi, G; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/391713
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