On the weak and strong convergence of the proximal point algorithm in reflexive Banach spaces. (2nd September 2017)

• Record Type: Journal Article
• Authors: Dadashi, Vahid; Khatibzadeh, Hadi
• Is Part Of: Optimization. Volume 66:Number 9(2017)
• Page Start: 1487
• Page End: 1494
• Publication Date: 2017-09-02
• Subjects: Proximal point algorithm -- maximal monotone operator -- -strongly monotone -- -generalized monotone -- -expansive operator -- equilibrium problems; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1337764
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, some proximal point algorithms (PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs with some assumptions. We can also get zero of maximal -expansive operator and maximal -monotone at zero operator using this method and then we apply it for finding a solution of the equilibrium problem.