Quasi-equilibrium problems (QEPs) allow a change of the feasible region together with the considered point, in contrast to standard equilibrium problems (EPs). In this work, we extend the Newton-type method for EPs considered by Santos et al. to the setting of QEPs. We prove locally the convergence of the method and we establish the superlinear/quadratic convergence of the algorithm to a solution of the problem under suitable assumptions. Applications to generalized Nash equilibrium problems (GNEPs) are considered. Some preliminary numerical results are reported showing the performance of the algorithm.

中文翻译：

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拟平衡问题的牛顿型方法及其应用

与标准平衡问题 (EP) 相比，准平衡问题 (QEP) 允许改变可行区域以及所考虑的点。在这项工作中，我们扩展了 Santos 等人考虑的 EP 的牛顿型方法。到 QEP 的设置。我们在局部证明了该方法的收敛性，并在适当的假设下建立了算法的超线性/二次收敛性以解决问题。考虑了对广义纳什均衡问题 (GNEP) 的应用。报告了一些初步的数值结果，显示了算法的性能。