Tseng's Algorithm with Extrapolation from the past Endowed with Variable Metrics and Error Terms. (25th January 2023)

• Record Type: Journal Article
• Authors: Tongnoi, Buris
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 2(2023)
• Page Start: 87
• Page End: 123
• Publication Date: 2023-01-25
• Subjects: Convergence analysis -- iterative methods -- optimization problems -- resolvent operators -- Tseng's algorithm; 47H05 -- 49M29 -- 47N10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2158196
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we propose a variable metric version of Tseng's algorithm (the forward-backward-forward algorithm: FBF) combined with extrapolation from the past that includes error terms for finding a zero of the sum of a maximally monotone operator and a monotone Lipschitzian operator in Hilbert spaces. The algorithm, which is a modified forward-reflected-backword method, is endowed with variable metrics and error terms. Primal-dual algorithms are also proposed for monotone inclusion problems involving compositions with linear operators. The primal-dual problem occurring in image deblurring demonstrates an application of our theoretical results.