A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence

Yekini Shehu (), Lulu Liu (), Qiao-Li Dong () and Jen-Chih Yao ()
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Yekini Shehu: Zhejiang Normal University
Lulu Liu: Civil Aviation University of China
Qiao-Li Dong: Civil Aviation University of China
Jen-Chih Yao: China Medical University

Networks and Spatial Economics, 2022, vol. 22, issue 4, No 10, 959-990

Abstract: Abstract We study the forward-backward-forward splitting method with alternated inertial step in this paper. We consider under-relaxation and over-relaxation approaches to the proposed method and obtain weak convergence results in both cases in real Hilbert spaces. Linear convergence alongside priori and apriori error estimates are obtained under some standard assumptions. Finally, we give some numerical implementations and comparisons to support the theoretical analysis.

Keywords: Forward-backward-forward splitting; Alternated inertial step; Weak convergence; Linear convergence; Hilbert spaces; 47H05; 47J20; 47J25; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11067-022-09575-8

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