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Regularized Methods for the Split Feasibility Problem

Author

Listed:
  • Yonghong Yao
  • Wu Jigang
  • Yeong-Cheng Liou

Abstract

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP).

Suggested Citation

  • Yonghong Yao & Wu Jigang & Yeong-Cheng Liou, 2012. "Regularized Methods for the Split Feasibility Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:140679
    DOI: 10.1155/2012/140679
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    References listed on IDEAS

    as
    1. Yonghong Yao & Yeol Je Cho & Pei-Xia Yang, 2012. "An Iterative Algorithm for a Hierarchical Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    2. Yonghong Yao & Yeol Je Cho & Pei-Xia Yang, 2012. "An Iterative Algorithm for a Hierarchical Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    Citations

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    Cited by:

    1. Cuijie Zhang, 2012. "Strong Convergence Theorems for the Generalized Split Common Fixed Point Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Mohammad Eslamian & Abdul Latif, 2013. "General Split Feasibility Problems in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Zhangsong Yao & Arif Rafiq & Shin Min Kang & Li-Jun Zhu, 2014. "Iterative Algorithms for the Split Problem and Its Convergence Analysis," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Jing Zhao & Songnian He, 2012. "Strong Convergence of the Viscosity Approximation Process for the Split Common Fixed‐Point Problem of Quasi‐Nonexpansive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Zhangsong Yao & Sun Young Cho & Shin Min Kang & Li-Jun Zhu, 2014. "A Regularized Algorithm for the Proximal Split Feasibility Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Youli Yu & Shin Min Kang & Young Chel Kwun, 2014. "Relaxed Extragradient Algorithms for the Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    7. Songnian He & Wenlong Zhu, 2012. "A Note on Approximating Curve with 1‐Norm Regularization Method for the Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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