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Inertial Proximal Point Algorithms for Solving a Class of Split Feasibility Problems

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Abstract

We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces. In order to solve this problem, we introduce two new algorithms which are based on the inertial proximal point algorithm. We first establish a weak convergence theorem and a convergence rate for the first algorithm. Next, we also establish the strong convergence of sequences generated by the second algorithm. An application of our main theorems to solving the split minimum point problem with multiple output sets and a pertinent numerical example are also presented in Sects. 6 and 7, respectively.

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Acknowledgements

The authors are grateful to the editor and the anonymous referees for their useful comments and helpful suggestions.

Funding

The first author was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion (Grant 2001893) and by the Technion General Research Fund (Grant 2016723). The second author was supported by the Science and Technology Fund of TNU—Thai Nguyen University of Sciences.

Author information

Authors and Affiliations

  1. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

  2. Thai Nguyen University of Sciences, Thai Nguyen, Viet Nam

    Truong Minh Tuyen

  3. Thai Nguyen University of Technology, Thai Nguyen, Vietnam

    Phan Thi Van Huyen

Authors
  1. Simeon Reich
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  2. Truong Minh Tuyen
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  3. Phan Thi Van Huyen
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Contributions

All authors contributed to the study conception and design. The first draft of the manuscript was written by Simeon Reich and Minh Tuyen Truong and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Truong Minh Tuyen.

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Communicated by Shoham Sabach.

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Reich, S., Tuyen, T.M. & Van Huyen, P.T. Inertial Proximal Point Algorithms for Solving a Class of Split Feasibility Problems. J Optim Theory Appl 200, 951–977 (2024). https://doi.org/10.1007/s10957-023-02343-9

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  • DOI: https://doi.org/10.1007/s10957-023-02343-9

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