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On descent-projection method for solving the split feasibility problems

Author

Listed:
  • Abdellah Bnouhachem
  • Muhammad Noor
  • Mohamed Khalfaoui
  • Sheng Zhaohan

Abstract

Let Ω and C be nonempty, closed and convex sets in R n and R m respectively and A be an $${m \times n}$$ real matrix. The split feasibility problem is to find $${u \in \Omega}$$ with $${Au \in C.}$$ Many problems arising in the image reconstruction can be formulated in this form. In this paper, we propose a descent-projection method for solving the split feasibility problems. The method generates the new iterate by searching the optimal step size along the descent direction. Under certain conditions, the global convergence of the proposed method is proved. In order to demonstrate the efficiency of the proposed method, we provide some numerical results. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:627-639
    DOI: 10.1007/s10898-011-9782-2
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    Citations

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    Cited by:

    1. Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    2. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "A New Hybrid CQ Algorithm for the Split Feasibility Problem in Hilbert Spaces and Its Applications to Compressed Sensing," Mathematics, MDPI, vol. 7(9), pages 1-15, August.
    3. 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.

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