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Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications

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Abstract

In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.

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Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions which improve the paper. The research of the second author was supported by the National Natural Science Foundation of China under Grant No.11401152.

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Bing Tan

  2. Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang, China

    Xiaolong Qin

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China

    Xiaolong Qin

  4. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

    Jen-Chih Yao

  5. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Jen-Chih Yao

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  1. Bing Tan
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  2. Xiaolong Qin
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  3. Jen-Chih Yao
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Correspondence to Xiaolong Qin.

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Tan, B., Qin, X. & Yao, JC. Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications. J Sci Comput 87, 20 (2021). https://doi.org/10.1007/s10915-021-01428-9

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  • DOI: https://doi.org/10.1007/s10915-021-01428-9

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