A proximal point method for quasi-equilibrium problems in Hilbert spaces. (2nd January 2022)

• Record Type: Journal Article
• Authors: Santos, Pedro Jorge S.; Souza, João Carlos de O.
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 55
• Page End: 70
• Publication Date: 2022-01-02
• Subjects: Quasi-equilibrium problem -- equilibrium problem -- proximal point method -- monotone bifunction; 49M37 -- 65K15 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1810686
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we study the convergence of a proximal point method for solving quasi-equilibrium problems (QEP) in Hilbert spaces. We extent the method proposed by Moudafi [Proximal point algorithm extended to equilibrium problems. J Nat Geom. 1999;15(1-2):91–100] and Iusem and Sosa [Iterative algorithms for equilibrium problems. Optimization. 2003;52(3):301–316] to the more general context of quasi-equilibrium problems. In our method a quasi-equilibrium problem is solved by computing a solution of an equilibrium problem at each iteration. We obtain weak convergence of the sequence to a solution of the QEP under some mild assumptions. Some encouraging numerical experiments are presented to show the performance of the method.