A Newton-type method for quasi-equilibrium problems and applications. (2nd January 2022)

• Record Type: Journal Article
• Authors: Santos, Pedro Jorge S.; Santos, Paulo Sérgio M.; Scheimberg, Susana
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 7
• Page End: 32
• Publication Date: 2022-01-02
• Subjects: Quasi-equilibrium problem -- nonsmooth Newton method -- generalized Nash equilibrium problem -- quasi-variational inequality -- equilibrium problem; 49M37 -- 65K15 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1945052
• Languages: English
• ISSNs: 0233-1934

Abstract

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.