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

Author

Listed:
  • Meng Wen

    (Xi’an Jiaotong University
    Beijing Center for Mathematics and Information Interdisciplinary Sciences)

  • Jigen Peng

    (Xi’an Jiaotong University
    Beijing Center for Mathematics and Information Interdisciplinary Sciences)

  • Yuchao Tang

    (NanChang University)

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.

Suggested Citation

  • Meng Wen & Jigen Peng & Yuchao Tang, 2015. "A Cyclic and Simultaneous Iterative Method for Solving the Multiple-Sets Split Feasibility Problem," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 844-860, September.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0701-9
    DOI: 10.1007/s10957-014-0701-9
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    References listed on IDEAS

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    1. H. H. Bauschke & S. G. Kruk, 2004. "Reflection-Projection Method for Convex Feasibility Problems with an Obtuse Cone," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 503-531, March.
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    Cited by:

    1. Jinhua Wang & Yaohua Hu & Carisa Kwok Wai Yu & Xiaojun Zhuang, 2019. "A Family of Projection Gradient Methods for Solving the Multiple-Sets Split Feasibility Problem," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 520-534, November.
    2. Q. L. Dong & Y. C. Tang & Y. J. Cho & Th. M. Rassias, 2018. "“Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem," Journal of Global Optimization, Springer, vol. 71(2), pages 341-360, June.

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