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New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces

Author

Listed:
  • Haiying Li
  • Yulian Wu
  • Fenghui Wang
  • Xiaolong Qin

Abstract

The split feasibility problem SFP has received much attention due to its various applications in signal processing and image reconstruction. In this paper, we propose two inertial relaxed CQ algorithms for solving the split feasibility problem in real Hilbert spaces according to the previous experience of applying inertial technology to the algorithm. These algorithms involve metric projections onto half-spaces, and we construct new variable step size, which has an exact form and does not need to know a prior information norm of bounded linear operators. Furthermore, we also establish weak and strong convergence of the proposed algorithms under certain mild conditions and present a numerical experiment to illustrate the performance of the proposed algorithms.

Suggested Citation

  • Haiying Li & Yulian Wu & Fenghui Wang & Xiaolong Qin, 2021. "New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, February.
    • Handle: RePEc:hin:jjmath:6624509
    DOI: 10.1155/2021/6624509
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    Cited by:

    1. Che, Haitao & Liu, Kaiping & Chen, Haibin & Yan, Hong, 2023. "Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Liya Liu & Tiexiang Li & Xiaolong Qin, 2026. "Halpern-type Bregman Projection Algorithms for Split Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-33, January.
    3. Yang Liu & Yazheng Dang & Kang Liu, 2025. "Inertial CQ Algorithm With Correction Terms for Split Feasibility Problems With Multiple Output Sets," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    4. Peeyada, Pronpat & Suparatulatorn, Raweerote & Cholamjiak, Watcharaporn, 2022. "An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    6. Haiying Li & Jiaoying He & Fenghui Wang, 2026. "Multi-step inertial algorithms for equilibrium, fixed point, general systems of variational inequalities and split feasibility problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 57(2), pages 597-627, April.

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