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Self-adaptive relaxed CQ algorithms for solving split feasibility problem with multiple output sets

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Abstract

In this paper, we propose two new self-adaptive relaxed CQ algorithms to solve the split feasibility problem with multiple output sets, which involve the computation of projections onto half-spaces instead of the computation onto the closed convex sets. Our proposed algorithms with selection technique reduce the computation of projections. And then, as a generalization, we construct two new algorithms to solve the variational inequalities over the solution set of split feasibility problem with multiple output sets. More importantly, strong convergence of all proposed algorithms is proved under suitable conditions. Finally, we conduct numerical experiments to show the efficiency and accuracy of our algorithms compared to some existing results.

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Author notes

  1. Tong Ling and Luoyi Shi have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Xiaolei Tong & Tong Ling

  2. School of Software, Tiangong University, Tianjin, 300387, China

    Luoyi Shi

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  1. Xiaolei Tong
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  2. Tong Ling
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  3. Luoyi Shi
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Correspondence to Luoyi Shi.

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Tong, X., Ling, T. & Shi, L. Self-adaptive relaxed CQ algorithms for solving split feasibility problem with multiple output sets. J. Appl. Math. Comput. 70, 1441–1469 (2024). https://doi.org/10.1007/s12190-024-02008-4

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  • DOI: https://doi.org/10.1007/s12190-024-02008-4

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