New strong convergence method for the sum of two maximal monotone operators

Y. Shehu, Q.-L. Dong, L.-L. Liu, J.-C. Yao, Optimization and Engineering (2020).

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Journal Article | Epub ahead of print | English

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Author
Shehu, YekiniIST Austria ; Dong, Qiao-Li; Liu, Lu-Lu; Yao, Jen-Chih
Department
Abstract
This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.
Publishing Year
Date Published
2020-07-31
Journal Title
Optimization and Engineering
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria). The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7—2007–2013) (Grant Agreement No. 616160). The authors are grateful to the anonymous referees and the handling Editor for their comments and suggestions which have improved the earlier version of the manuscript greatly.
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Cite this

Shehu Y, Dong Q-L, Liu L-L, Yao J-C. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. 2020. doi:10.1007/s11081-020-09544-5
Shehu, Y., Dong, Q.-L., Liu, L.-L., & Yao, J.-C. (2020). New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering. https://doi.org/10.1007/s11081-020-09544-5
Shehu, Yekini, Qiao-Li Dong, Lu-Lu Liu, and Jen-Chih Yao. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering, 2020. https://doi.org/10.1007/s11081-020-09544-5.
Y. Shehu, Q.-L. Dong, L.-L. Liu, and J.-C. Yao, “New strong convergence method for the sum of two maximal monotone operators,” Optimization and Engineering, 2020.
Shehu Y, Dong Q-L, Liu L-L, Yao J-C. 2020. New strong convergence method for the sum of two maximal monotone operators. Optimization and Engineering.
Shehu, Yekini, et al. “New Strong Convergence Method for the Sum of Two Maximal Monotone Operators.” Optimization and Engineering, Springer Nature, 2020, doi:10.1007/s11081-020-09544-5.
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