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Modified general splitting method for the split feasibility problem

Author

Listed:
  • Seakweng Vong

    (University of Macau)

  • Zhongsheng Yao

    (University of Macau
    Guangdong Ocean University)

Abstract

Based on the equivalent optimization problems of the splitting feasibility problem, we investigate this problem by using modified general splitting method in this paper. One is a relaxation splitting method with linearization, and the other combines the former with alternated inertial extrapolation step. The strong convergence of our algorithms is analyzed when related parameters are properly chosen. Compared with most existing results where inertial factor must be less than 1, inertial factor can be taken 1 in our alternated inertial-type algorithm. The efficiency of our methods are illustrated by some numerical examples.

Suggested Citation

  • Seakweng Vong & Zhongsheng Yao, 2024. "Modified general splitting method for the split feasibility problem," Journal of Global Optimization, Springer, vol. 90(3), pages 711-726, November.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:3:d:10.1007_s10898-024-01399-9
    DOI: 10.1007/s10898-024-01399-9
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    References listed on IDEAS

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    1. Wenxing Zhang & Deren Han & Xiaoming Yuan, 2012. "An efficient simultaneous method for the constrained multiple-sets split feasibility problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 825-843, July.
    2. Franck Iutzeler & Jérôme Malick, 2018. "On the Proximal Gradient Algorithm with Alternated Inertia," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 688-710, March.
    3. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
    4. 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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