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

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 apr...

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Bibliographic Details
Published in:Networks and spatial economics Vol. 22; no. 4; pp. 959 - 990
Main Authors: Shehu, Yekini, Liu, Lulu, Dong, Qiao-Li, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2022
Springer Nature B.V
Subjects:
Algorithms
Civil Engineering
Convergence
Economic activity
Economics
Economics and Finance
Hilbert space
Methods
Operations Research/Decision Theory
Regional/Spatial Science
Weak convergence
Alternated inertial step
Linear convergence
65K15
47J20
90C25
Forward-backward-forward splitting
Hilbert spaces
47H05
47J25
ISSN:1566-113X, 1572-9427
Online Access:Get full text
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Summary: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.
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ISSN:1566-113X
1572-9427
DOI:10.1007/s11067-022-09575-8