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The Generalized Fermat–Torricelli Problem in Hilbert Spaces

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Abstract

We study the generalized Fermat–Torricelli problem and the split feasibility problem with multiple output sets in Hilbert spaces. We first introduce the generalized Fermat–Torricelli problem, and propose and analyze a subgradient algorithm for solving this model problem. Then we study the convergence of variants of our proposed algorithm for solving the split feasibility problem with multiple output sets. Our algorithms for solving this problem are completely different from previous ones because we do not use the least squares sum method.

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Acknowledgements

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 and by the Technion General Research Fund. The second author was supported by the Science and Technology Fund of the Vietnam Ministry of Education and Training (B2022-TNA-23). Both authors are grateful to two anonymous referees for their useful comments and helpful suggestions.

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Authors and Affiliations

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

    Simeon Reich

  2. Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen, Vietnam

    Truong Minh Tuyen

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  1. Simeon Reich
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  2. Truong Minh Tuyen
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Correspondence to Truong Minh Tuyen.

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Communicated by Heinz Bauschke.

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Reich, S., Tuyen, T.M. The Generalized Fermat–Torricelli Problem in Hilbert Spaces. J Optim Theory Appl 196, 78–97 (2023). https://doi.org/10.1007/s10957-022-02113-z

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  • DOI: https://doi.org/10.1007/s10957-022-02113-z

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