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Two Relaxed CQ Methods for the Split Feasibility Problem with Multiple Output Sets

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Abstract

In this paper, two relaxed CQ algorithms with non-inertial and inertial steps are proposed for solving the split feasibility problems with multiple output sets (SFPMOS) in infinite-dimensional real Hilbert spaces. The step size is determined dynamically without requiring prior information about the operator norm. Furthermore, the proposed algorithms are proven to converge strongly to the minimum-norm solution of the SFPMOS. Some applications of our main results regarding the solution of the split feasibility problem are presented. Finally, we give two numerical examples to illustrate the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature.

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Acknowledgements

The authors would like to thank the referees and the editor for their valuable comments and suggestions which improve the presentation of this manuscript.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nguyen Thi Thu Thuy & Tran Thanh Tung

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  1. Nguyen Thi Thu Thuy
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  2. Tran Thanh Tung
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The authors contributed equally to this work.

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Correspondence to Nguyen Thi Thu Thuy.

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Communicated by Anton Abdulbasah Kamil.

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Thuy, N.T.T., Tung, T.T. Two Relaxed CQ Methods for the Split Feasibility Problem with Multiple Output Sets. Bull. Malays. Math. Sci. Soc. 47, 68 (2024). https://doi.org/10.1007/s40840-023-01647-3

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  • DOI: https://doi.org/10.1007/s40840-023-01647-3

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