Published in: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 . 2021;22:2627-2653. doi: 10.1007/s11081-020-09544-5
Language:
English
DOI:
https://doi.org/10.1007/s11081-020-09544-5
ISSN:
1389-4420;
1573-2924
Origination:
Footnote:
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Description:
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.