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Open AccessArticle

Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem

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Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
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Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan P.O. Box 445, Ethiopia
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Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
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Author to whom correspondence should be addressed.
Math. Comput. Appl. 2020, 25(3), 47; https://doi.org/10.3390/mca25030047
Received: 3 June 2020 / Revised: 19 July 2020 / Accepted: 21 July 2020 / Published: 24 July 2020
In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature. View Full-Text
Keywords: multiple-set split feasibility problem; relaxed CQ algorithm; subdifferential; strong convergence; Hilbert space multiple-set split feasibility problem; relaxed CQ algorithm; subdifferential; strong convergence; Hilbert space
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MDPI and ACS Style

Taddele, G.H.; Kumam, P.; Gebrie, A.G.; Sitthithakerngkiet, K. Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem. Math. Comput. Appl. 2020, 25, 47. https://doi.org/10.3390/mca25030047

AMA Style

Taddele GH, Kumam P, Gebrie AG, Sitthithakerngkiet K. Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem. Mathematical and Computational Applications. 2020; 25(3):47. https://doi.org/10.3390/mca25030047

Chicago/Turabian Style

Taddele, Guash H.; Kumam, Poom; Gebrie, Anteneh G.; Sitthithakerngkiet, Kanokwan. 2020. "Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem" Math. Comput. Appl. 25, no. 3: 47. https://doi.org/10.3390/mca25030047

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