Abstract
We come up with a new type of forward–backward–forward algorithms for monotone inclusion problems based on a self-adaptive technique to avoid the selection of Lipschitz assumption and also double inertial extrapolations to increase the convergence performance of our presented algorithm. We also prove its weak convergence theorem under mild hypothesis. Additionally, we provide numerical test in image deblurring and signal recovery as applications. The results show that our algorithm outperforms some known algorithms in the literature.
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Acknowledgements
The authors sincerely thank the anonymous reviewers for their suggestions that improve the manuscript substantially. P. Cholamjiak was supported by the National Research Council of Thailand under grant no. N41A640094, the Thailand Science Research and Innovation Fund, and the University of Phayao under the project FF66-UoE. Moreover, S. Suantai has received funding support from the NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation [grant number B05F640183]. It was also partially supported by Chiang Mai University.
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Suantai, S., Inkrong, P. & Cholamjiak, P. Forward–backward–forward algorithms involving two inertial terms for monotone inclusions. Comp. Appl. Math. 42, 255 (2023). https://doi.org/10.1007/s40314-023-02388-6
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DOI: https://doi.org/10.1007/s40314-023-02388-6