Reflected three-operator splitting method for monotone inclusion problem. (4th July 2022)

• Record Type: Journal Article
• Authors: Iyiola, Olaniyi S.; Enyi, Cyril D.; Shehu, Yekini
• Is Part Of: Optimization methods and software. Volume 37:Number 4(2022)
• Page Start: 1527
• Page End: 1565
• Publication Date: 2022-07-04
• Subjects: Reflected Krasnosel'skiĭ-Mann -- weak convergence -- sublinear rate -- reflected three-operator splitting -- reflected primal-dual -- Hilbert spaces; 47H05 -- 47J20 -- 47J25 -- 65K15 -- 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1924715
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O ( 1 / n ) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.