A proximal point method for quasi-equilibrium problems in Hilbert spaces

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 algor...

Full description

Saved in:
Bibliographic Details
Published inOptimization Vol. 71; no. 1; pp. 55 - 70
Main Authors Santos, Pedro Jorge S., Souza, João Carlos de O.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.01.2022
Taylor & Francis LLC
Subjects
Convergence
Equilibrium
equilibrium problem
Hilbert space
Iterative algorithms
Iterative methods
monotone bifunction
Optimization
proximal point method
Quasi-equilibrium problem
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1810686