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Linear approximation method for solving split inverse problems and its applications

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Abstract

We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the proposed scheme is established under mild assumptions and several synthetic and practical numerical illustrations demonstrate the validity and advantages of our method compared with related schemes 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 was 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). We are also very grateful to the Editor and Reviewers for taking the time and effort necessary to review the manuscript. We sincerely appreciate all valuable comments and suggestions, which helped us to improve the quality of the manuscript.

Funding

This research was funded by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, KMUTT. The first author was supported by the ”Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi” with 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

  2. College of Science, Civil Aviation University of China, Tianjin, China

    Yuan Li & Jing Zhao

  3. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  4. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

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  1. Guash Haile Taddele
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  2. Yuan Li
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  3. Aviv Gibali
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  4. Poom Kumam
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  5. Jing Zhao
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Correspondence to Poom Kumam.

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Taddele, G.H., Li, Y., Gibali, A. et al. Linear approximation method for solving split inverse problems and its applications. Adv Comput Math 48, 39 (2022). https://doi.org/10.1007/s10444-022-09959-x

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