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Inertial proximal point algorithm for the split common solution problem of monotone operator equations

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Abstract

This paper provides a new approach to solving the class of split problems. More precisely, we investigate the split common solution problem for monotone operator equations in real Hilbert spaces. To find a solution to this problem, we propose three new iterative algorithms. These algorithms are established based on the inertial proximal point algorithm. We prove the weak convergence of the first algorithm. Next, to obtain the strong convergence theorems, in the second and the third ones, we combine the first algorithms with the hybrid projection method or the shrinking projection method, respectively. Some applications of the main theorems for solving related problems are also presented. Two numerical examples are also given to illustrate the effectiveness of the proposed algorithms.

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Acknowledgements

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

Funding

This research was supported by Project of the TNU-University of Sciences in Vietnam under Grant No. CS2022-TN06-03.

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Authors and Affiliations

  1. Thainguyen University of Sciences, Thainguyen, Vietnam

    Nguyen Song Ha & Truong Minh Tuyen

  2. Thainguyen University of Technology, Thainguyen, Vietnam

    Phan Thi Van Huyen

Authors
  1. Nguyen Song Ha
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  2. Truong Minh Tuyen
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  3. Phan Thi Van Huyen
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Contributions

All authors have contributed to the study conception and design. The first draft of the manuscript was written by Minh Tuyen Truong and Song Ha Nguyen, 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 Joerg Fliege.

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Song Ha, N., Minh Tuyen, T. & Thi Van Huyen, P. Inertial proximal point algorithm for the split common solution problem of monotone operator equations. Comp. Appl. Math. 42, 303 (2023). https://doi.org/10.1007/s40314-023-02441-4

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  • DOI: https://doi.org/10.1007/s40314-023-02441-4

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