On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems

We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert spaces. The proposed algorithms work adaptively in the absence of the Lipschitz constant of the single-valued operator involved thanks to the fact that...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 4
Main Authors Tan, Bing, Qin, Xiaolong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2024
Springer Nature B.V
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convergence
Hilbert space
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
Monotone inclusion
65K15
47J20
49J40
90C33
68W10
Convergence rate
Inclusion problem
Forward-backward method
Projection and contraction method
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Summary:We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert spaces. The proposed algorithms work adaptively in the absence of the Lipschitz constant of the single-valued operator involved thanks to the fact that there is a non-monotonic step size criterion used. The weak and strong convergence and the R -linear convergence of the developed algorithms are investigated under some appropriate assumptions. Finally, our algorithms are put into practice to address the restoration problem in the signal and image fields, and they are compared to some pertinent algorithms in the literature.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10156-1