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An extended inertial Halpern-type ball-relaxed CQ algorithm for multiple-sets split feasibility problem

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Abstract

In an infinite-dimensional real Hilbert space setting, we introduce a new self-adaptive inertial Halpern-type projection algorithm for solving multiple-sets split feasibility problem assuming that the involved convex subsets are level subsets of strongly convex functions by approximating the original convex subsets by a sequence of closed balls instead of half-spaces. Since the projection onto the closed ball has a closed form, the proposed algorithm is hence easy to implement. Moreover, we construct a new self-adaptive stepsize that is bounded away from zero and is independent of the operator norm. Under some mild assumptions and without the usual Lipschitz’s continuity of the gradient operator assumption, we establish and prove a strong convergence of the sequence generated by the proposed algorithm. Several numerical illustrations indicate that the proposed algorithm is computationally efficient and competes well with some existing algorithms in the literature. The proposed method is an improvement and generalization of many results in the literature.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Guash Haile Taddele is supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi (Grant no. 37/2561). Moreover, this project is funded by National Research Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Guash Haile Taddele & Poom Kumam

  2. Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Faculty of Science, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Guash Haile Taddele & Poom Kumam

  3. Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Centre, Victoriei 76, 430122, Baia Mare, Romania

    Vasile Berinde

  4. Department of Medical Research , China Medical University Hospital China Medical University , 40402, Taichung, Taiwan

    Poom Kumam

  5. Academy of Romanian Scientists , Ilfov Str. no. 3, 050045, Bucharest, Romania

    Vasile Berinde

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  1. Guash Haile Taddele
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  2. Poom Kumam
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  3. Vasile Berinde
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All authors contributed equally to the manuscript and read and approved the final manuscript.

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Correspondence to Poom Kumam.

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Communicated by Constantin Niculescu.

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Taddele, G.H., Kumam, P. & Berinde, V. An extended inertial Halpern-type ball-relaxed CQ algorithm for multiple-sets split feasibility problem. Ann. Funct. Anal. 13, 48 (2022). https://doi.org/10.1007/s43034-022-00190-9

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