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Two relaxed inertial forward-backward-forward algorithms for solving monotone inclusions and an application to compressed sensing

Part of: Algorithms - Computer Science Existence theories Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  13 January 2025

Bing Tan Open the ORCID record for Bing Tan [Opens in a new window]  and
Xiaolong Qin Open the ORCID record for Xiaolong Qin [Opens in a new window]
Bing Tan
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing, China e-mail: bingtan@swu.edu.cn bingtan72@gmail.com URL: https://bingtan.me/
Xiaolong Qin*
Affiliation:
Department of Mathematics, Hangzhou Normal University, Hangzhou, China; Nanjing Center for Applied Mathematics, Nanjing, China
*
e-mail: qxlxajh@163.com
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Abstract

Two novel algorithms, which incorporate inertial terms and relaxation effects, are introduced to tackle a monotone inclusion problem. The weak and strong convergence of the algorithms are obtained under certain conditions, and the R-linear convergence for the first algorithm is demonstrated if the set-valued operator involved is strongly monotone in real Hilbert spaces. The proposed algorithms are applied to signal recovery problems and demonstrate improved performance compared to existing algorithms in the literature.

Keywords

Inclusion problemsmonotone operatorsignal recoveryforward-backward-forward methodconvergence rate

MSC classification

Primary: 47J20: Variational and other types of inequalities involving nonlinear operators (general)
Secondary: 49J40: Variational methods including variational inequalities 65K15: Numerical methods for variational inequalities and related problems 68W10: Parallel algorithms 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions)
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

B. Tan thanks the support of the Natural Science Foundation of Chongqing (No. CSTB2024NSCQ-MSX0354), the National Natural Science Foundation of China (No. 12471473), and the Fundamental Research Funds for the Central Universities (No. SWU-KQ24052).

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