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Iterative Regularization Methods for the Multiple-Sets Split Feasibility Problem in Hilbert Spaces

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Abstract

In this paper, we introduce iterative regularization methods for solving the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a bounded linear mapping will be closest to another family of closed convex subsets in the image space. We consider the cases, when the families are either finite or infinite. We also give two numerical examples for illustrating our main method.

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Acknowledgements

The authors are extremely grateful to the referees for their useful comments, which helped to improve this paper. This work was supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.02-2017.305.

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Authors and Affiliations

  1. Duy Tan University, 13 Quang Trung, Da Nang, Vietnam

    Nguyen Buong

  2. Vietnam Academy of Science and Technology, Institute of Information Technology, 18, Hoang Quoc Viet, Hanoi, Vietnam

    Nguyen Buong

  3. Vietnam Maritime University, Hai Phong, Vietnam

    Pham Thi Thu Hoai

  4. Banking Academy, Hanoi, Vietnam

    Khuat Thi Binh

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  1. Nguyen Buong
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  2. Pham Thi Thu Hoai
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  3. Khuat Thi Binh
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Correspondence to Nguyen Buong.

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Buong, N., Hoai, P.T.T. & Thi Binh, K. Iterative Regularization Methods for the Multiple-Sets Split Feasibility Problem in Hilbert Spaces. Acta Appl Math 165, 183–197 (2020). https://doi.org/10.1007/s10440-019-00249-1

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