Reflected three-operator splitting method for monotone inclusion problem

Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software.

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Journal Article | Epub ahead of print | English

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Author
Iyiola, Olaniyi S.; Enyi, Cyril D.; Shehu, YekiniIST Austria
Department
Abstract
In this paper, we consider reflected three-operator splitting methods for monotone inclusion problems in real Hilbert spaces. To do this, we first obtain weak convergence analysis and nonasymptotic O(1/n) convergence rate of the reflected Krasnosel'skiĭ-Mann iteration for finding a fixed point of nonexpansive mapping in real Hilbert spaces under some seemingly easy to implement conditions on the iterative parameters. We then apply our results to three-operator splitting for the monotone inclusion problem and consequently obtain the corresponding convergence analysis. Furthermore, we derive reflected primal-dual algorithms for highly structured monotone inclusion problems. Some numerical implementations are drawn from splitting methods to support the theoretical analysis.
Publishing Year
Date Published
2021-05-12
Journal Title
Optimization Methods and Software
Acknowledgement
The authors are grateful to the anonymous referees and the handling Editor for their insightful comments which have improved the earlier version of the manuscript greatly. The second author is grateful to the University of Hafr Al Batin. The last author has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP7-2007-2013) (Grant agreement No. 616160).
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Cite this

Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. 2021. doi:10.1080/10556788.2021.1924715
Iyiola, O. S., Enyi, C. D., & Shehu, Y. (2021). Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software. Taylor and Francis. https://doi.org/10.1080/10556788.2021.1924715
Iyiola, Olaniyi S., Cyril D. Enyi, and Yekini Shehu. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software. Taylor and Francis, 2021. https://doi.org/10.1080/10556788.2021.1924715.
O. S. Iyiola, C. D. Enyi, and Y. Shehu, “Reflected three-operator splitting method for monotone inclusion problem,” Optimization Methods and Software. Taylor and Francis, 2021.
Iyiola OS, Enyi CD, Shehu Y. 2021. Reflected three-operator splitting method for monotone inclusion problem. Optimization Methods and Software.
Iyiola, Olaniyi S., et al. “Reflected Three-Operator Splitting Method for Monotone Inclusion Problem.” Optimization Methods and Software, Taylor and Francis, 2021, doi:10.1080/10556788.2021.1924715.

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