## Abstract

Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.

Original language | English |
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Pages (from-to) | 373-397 |

Number of pages | 25 |

Journal | Journal of Global Optimization |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2013 |

## Keywords

- Generalized Nash equilibrium problems
- Hybrid extragradient methods
- Quasi-equilibrium problems
- Quasi-variational inequalities