A method with inertial extrapolation step for split monotone inclusion problems. (3rd April 2021)

• Record Type: Journal Article
• Authors: Yao, Yonghong; Shehu, Yekini; Li, Xiao-Huan; Dong, Qiao-Li
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 741
• Page End: 761
• Publication Date: 2021-04-03
• Subjects: Split monotone inclusion -- inertial extrapolation step -- weak convergence -- numerical examples -- Hilbert spaces; 47H05 -- 47J20 -- 47J25 -- 65K15 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1857754
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The purpose of this paper is to study the convergence analysis of an iterative algorithm with inertial extrapolation step for finding an approximate solution of split monotone inclusion problem in real Hilbert spaces. Weak convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. Some special cases of the general problem are given and we give some numerical implementations to support the theoretical analysis and give justification for the addition of the extrapolation step in the proposed method.