On the inertial forward-backward splitting technique for solving a system of inclusion problems in Hilbert spaces. (2nd December 2021)

• Record Type: Journal Article
• Authors: Chang, Shih-sen; Yao, Jen-Chih; Wang, Lin; Liu, Min; Zhao, Liangcai
• Is Part Of: Optimization. Volume 70:Number 12(2021)
• Page Start: 2511
• Page End: 2525
• Publication Date: 2021-12-02
• Subjects: Inertial forward-backward splitting technique -- maximal monotone operators -- inverse strongly monotone operator -- monotone inclusion -- averaged operator; 26A18 -- 47H04 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1786567
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The purpose of this paper is to introduce and study the existence problem of solution for a system of monotone variational inclusion problems in Hilbert spaces. By using the inertial forward-backward splitting technique, we propose and analyze an algorithm. Under suitable conditions, we proved that the sequence generated by the algorithm converges strongly to a solution of such kind of monotone variational inclusion problems. At the end of the paper, some applications are also given. The results presented in the paper extend and improve some recent results.