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Analysis on Newton projection method for the split feasibility problem

Author

Listed:
  • Biao Qu

    (Qufu Normal University)

  • Changyu Wang

    (Qufu Normal University)

  • Naihua Xiu

    (Beijing Jiaotong University)

Abstract

In this paper, based on a merit function of the split feasibility problem (SFP), we present a Newton projection method for solving it and analyze the convergence properties of the method. The merit function is differentiable and convex. But its gradient is a linear composite function of the projection operator, so it is nonsmooth in general. We prove that the sequence of iterates converges globally to a solution of the SFP as long as the regularization parameter matrix in the algorithm is chosen properly. Especially, under some local assumptions which are necessary for the case where the projection operator is nonsmooth, we prove that the sequence of iterates generated by the algorithm superlinearly converges to a regular solution of the SFP. Finally, some numerical results are presented.

Suggested Citation

  • Biao Qu & Changyu Wang & Naihua Xiu, 2017. "Analysis on Newton projection method for the split feasibility problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 175-199, May.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:1:d:10.1007_s10589-016-9884-3
    DOI: 10.1007/s10589-016-9884-3
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    References listed on IDEAS

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    1. Qu, Biao & Liu, Binghua & Zheng, Na, 2015. "On the computation of the step-size for the CQ-like algorithms for the split feasibility problem," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 218-223.
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    Cited by:

    1. Li-Jun Zhu & Yonghong Yao, 2019. "An Iterative Approach to the Solutions of Proximal Split Feasibility Problems," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    2. Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.

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