A Newton-type method for quasi-equilibrium problems and applications

Abstract

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.

Keywords:

• Quasi-equilibrium problem
• nonsmooth Newton method
• generalized Nash equilibrium problem
• quasi-variational inequality
• equilibrium problem

AMS CLASSIFICATIONS:

• 49M37
• 65K15
• 90C33

Disclosure statement

No potential conflict of interest was reported by the authors.