Proximal point algorithm for infinite pseudo-monotone bifunctions. (2nd August 2016)

• Record Type: Journal Article
• Authors: Khatibzadeh, Hadi; Mohebbi, Vahid
• Is Part Of: Optimization. Volume 65:Number 8(2016)
• Page Start: 1629
• Page End: 1639
• Publication Date: 2016-08-02
• Subjects: Equilibrium problem -- pseudo-monotone bifunction -- proximal point algorithm -- weak convergence -- strong convergence -- Halpern's method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1153639
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, first we study the weak convergence of the proximal point algorithm for an infinite family of equilibrium problems of pseudo-monotone type in Hilbert spaces. Then with additional conditions on the bifunctions, we prove the strong convergence for the family to a common equilibrium point. We also study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point of the family of infinite pseudo-monotone bifunctions without any additional assumptions on the bifunctions. A concrete example of a family of pseudo-monotone bifunctions is also presented.