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“Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem

Author

Listed:
  • Q. L. Dong

    (Civil Aviation University of China)

  • Y. C. Tang

    (NanChang University)

  • Y. J. Cho

    (University of Electronic Science and Technology of China
    Gyeongsang National University)

  • Th. M. Rassias

    (National Technical University of Athens)

Abstract

In this paper, first, we review the projection and contraction methods for solving the split feasibility problem (SFP), and then by using the inverse strongly monotone property of the underlying operator of the SFP, we improve the “optimal” step length to provide the modified projection and contraction methods. Also, we consider the corresponding relaxed variants for the modified projection and contraction methods, where the two closed convex sets are both level sets of convex functions. Some convergence theorems of the proposed methods are established under suitable conditions. Finally, we give some numerical examples to illustrate that the modified projection and contraction methods have an advantage over other methods, and improve greatly the projection and contraction methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:2:d:10.1007_s10898-018-0628-z
    DOI: 10.1007/s10898-018-0628-z
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    References listed on IDEAS

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    1. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    2. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
    3. Abdellah Bnouhachem & Muhammad Noor & Mohamed Khalfaoui & Sheng Zhaohan, 2012. "On descent-projection method for solving the split feasibility problems," Journal of Global Optimization, Springer, vol. 54(3), pages 627-639, November.
    4. 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.
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    Cited by:

    1. Yan-Juan He & Li-Jun Zhu & Nan-Nan Tan, 2021. "An Improved Alternating CQ Algorithm for Solving Split Equality Problems," Mathematics, MDPI, vol. 9(24), pages 1-10, December.
    2. Dang Van Hieu & Jean Jacques Strodiot & Le Dung Muu, 2020. "An Explicit Extragradient Algorithm for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 476-503, May.
    3. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.

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