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Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem

Received: 6 February 2017     Accepted: 1 March 2017     Published: 24 March 2017
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Abstract

In this paper, we present several explicit and hybrid strong convergence algorithms for solving the multiple-sets split feasibility problem (MSSFP). Firstly, we modify the existing successive, parallel and cyclic algorithms with the hybrid steepest descent method; then two new hybrid formulas based on the Mann type method are presented; Two general hybrid algorithms which can cover the former ones are further proposed. Strong convergence properties are investigated, and numerical experiments shows the compromise is promising.

Published in International Journal of Discrete Mathematics (Volume 2, Issue 3)
DOI 10.11648/j.dmath.20170203.14
Page(s) 80-87
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Variational Inequalities, Multiple-Sets Split Feasibility Problem, Hybrid Steepest Descent Method, Lipschitz Continuous, Inverse Strongly Monotone

References
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[15] H. He, S. Liu and M. A. Noor, “Some Krasnonsel’ski-Mann Algorithms and the Multiple-Set Split Feasibility Problem”, Fixed Point Theory and Applications, 2010, DOI: 10.1155/2010/513956.
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[17] F. E. Browder, “Fixed point theorems for noncompact mappings in Hilbert space”, Proc, Natl Acad. Sci. USA, 1965, vol. 53, pp. 1272–1276.
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Cite This Article
  • APA Style

    Peiyuan Wang, Jianjun Zhou, Risheng Wang, Jie Chen. (2017). Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem. International Journal of Discrete Mathematics, 2(3), 80-87. https://doi.org/10.11648/j.dmath.20170203.14

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    ACS Style

    Peiyuan Wang; Jianjun Zhou; Risheng Wang; Jie Chen. Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem. Int. J. Discrete Math. 2017, 2(3), 80-87. doi: 10.11648/j.dmath.20170203.14

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    AMA Style

    Peiyuan Wang, Jianjun Zhou, Risheng Wang, Jie Chen. Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem. Int J Discrete Math. 2017;2(3):80-87. doi: 10.11648/j.dmath.20170203.14

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  • @article{10.11648/j.dmath.20170203.14,
      author = {Peiyuan Wang and Jianjun Zhou and Risheng Wang and Jie Chen},
      title = {Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {3},
      pages = {80-87},
      doi = {10.11648/j.dmath.20170203.14},
      url = {https://doi.org/10.11648/j.dmath.20170203.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170203.14},
      abstract = {In this paper, we present several explicit and hybrid strong convergence algorithms for solving the multiple-sets split feasibility problem (MSSFP). Firstly, we modify the existing successive, parallel and cyclic algorithms with the hybrid steepest descent method; then two new hybrid formulas based on the Mann type method are presented; Two general hybrid algorithms which can cover the former ones are further proposed. Strong convergence properties are investigated, and numerical experiments shows the compromise is promising.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Some Explicit and Hybrid Strong Convergence Algorithms for Solving the Multiple-Sets Split Feasibility Problem
    AU  - Peiyuan Wang
    AU  - Jianjun Zhou
    AU  - Risheng Wang
    AU  - Jie Chen
    Y1  - 2017/03/24
    PY  - 2017
    N1  - https://doi.org/10.11648/j.dmath.20170203.14
    DO  - 10.11648/j.dmath.20170203.14
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 80
    EP  - 87
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20170203.14
    AB  - In this paper, we present several explicit and hybrid strong convergence algorithms for solving the multiple-sets split feasibility problem (MSSFP). Firstly, we modify the existing successive, parallel and cyclic algorithms with the hybrid steepest descent method; then two new hybrid formulas based on the Mann type method are presented; Two general hybrid algorithms which can cover the former ones are further proposed. Strong convergence properties are investigated, and numerical experiments shows the compromise is promising.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • Postdoctoral Workstation, China Marine Development and Reserch Center (CMDRC), Beijing, China

  • China Marine Development and Reserch Center (CMDRC), Beijing, China

  • China Marine Development and Reserch Center (CMDRC), Beijing, China

  • China Marine Development and Reserch Center (CMDRC), Beijing, China

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