Convergence Rate Analysis of Inertial Krasnoselskii–Mann Type Iteration with Applications. (27th July 2018)

• Record Type: Journal Article
• Authors: Shehu, Yekini
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 10(2018)
• Page Start: 1077
• Page End: 1091
• Publication Date: 2018-07-27
• Subjects: Convergence rate -- Hilbert spaces -- inertial terms -- nonexpansive mapping; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1477799
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: It is well known that the Krasnoselskii–Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii–Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas–Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii–Mann iteration in the literature.