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A strongly convergent Mann-type inertial algorithm for solving split variational inclusion problems

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Abstract

In this paper, we propose a new iterative method for finding an element of the solution set of a split variational inclusion problem in real Hilbert spaces. The iterative scheme is based on a well-known Mann-type method to obtain strong convergence and an inertial method to speed up the convergence rate. We also apply the proposed algorithm to studying the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithm is efficient and implementable from the numerical point of view.

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Acknowledgements

The authors would like to thank the Editor and the two referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper. This work was partially supported by the National Foundation for Science and Technology Development under Grant: 101.01-2019.320

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Authors and Affiliations

  1. Department of Mathematics, University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Pham Ky Anh & Vu Tien Dung

  2. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Duong Viet Thong

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  1. Pham Ky Anh
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  2. Duong Viet Thong
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  3. Vu Tien Dung
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Correspondence to Duong Viet Thong.

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Anh, P.K., Thong, D.V. & Dung, V.T. A strongly convergent Mann-type inertial algorithm for solving split variational inclusion problems. Optim Eng 22, 159–185 (2021). https://doi.org/10.1007/s11081-020-09501-2

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