Strong convergence of a generalized forward–backward splitting method in reflexive Banach spaces. (3rd June 2022)

• Record Type: Journal Article
• Authors: Minh Tuyen, Truong; Promkam, Ratthaprom; Sunthrayuth, Pongsakorn
• Is Part Of: Optimization. Volume 71:Number 6(2022)
• Page Start: 1483
• Page End: 1508
• Publication Date: 2022-06-03
• Subjects: Maximal monotone operator -- Legendre function -- reflexive banach space -- strong convergence -- Bregman inverse strongly monotone; 47H09 -- 47H10 -- 47J25 -- 47J05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1812607
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we study the so-called generalized monotone quasi-inclusion problem which is a generalization and extension of well-known monotone quasi-inclusion problem. We propose a forward–backward splitting method for solving this problem in the framework of reflexive Banach spaces. Based on Bregman distance function, we prove a strong convergence result of the proposed algorithm to a common zero of the problem. As an application, we apply the main result to the variational inequality problem. Finally, we provide some numerical examples to demonstrate our algorithm performance. The results presented in this paper improve and extend many known results in the literature.