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A Cyclic and Simultaneous Iterative Method for Solving the Multiple-Sets Split Feasibility Problem

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Abstract

The iterative projection methods for solving the multiple-sets split feasibility problem have been paid much attention in recent years. In this paper, we introduce a cyclic and simultaneous iterative sequence with self-adaptive step size for solving this problem. The advantage of the self-adaptive step size is that it does not need to know the Lipschitz constant of the gradient operator in advance. Furthermore, we propose a relaxed cyclic and simultaneous iterative sequence with self-adaptive step size, respectively. The theoretical convergence results are established in an infinite-dimensional Hilbert spaces setting. Preliminary numerical experiments show that these iteration methods are practical and easy to implement.

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Acknowledgments

This work was supported by the National Natural Science Foundations of China (11131006, 11201216, 11401293, 11461046), the National Basic Research Program of China (2013CB329404), and the Natural Science Foundations of Jiangxi Province (20142BAB211016).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Meng Wen & Jigen Peng

  2. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, People’s Republic of China

    Meng Wen & Jigen Peng

  3. Department of Mathematics, NanChang University, Nanchang, 330031, People’s Republic of China

    Yuchao Tang

Authors
  1. Meng Wen
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  2. Jigen Peng
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  3. Yuchao Tang
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Correspondence to Yuchao Tang.

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Wen, M., Peng, J. & Tang, Y. A Cyclic and Simultaneous Iterative Method for Solving the Multiple-Sets Split Feasibility Problem. J Optim Theory Appl 166, 844–860 (2015). https://doi.org/10.1007/s10957-014-0701-9

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  • DOI: https://doi.org/10.1007/s10957-014-0701-9

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