The Generalized Fermat–Torricelli Problem in Hilbert Spaces

Simeon Reich () and Truong Minh Tuyen ()
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Simeon Reich: The Technion – Israel Institute of Technology
Truong Minh Tuyen: Thai Nguyen University of Sciences

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 4, 78-97

Abstract: 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.

Keywords: Hilbert space; Fermat–Torricelli problem; Metric projection; 47H05; 47H09; 49J53; 90C25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02113-z

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