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Projection Algorithms for Solving the Split Feasibility Problem with Multiple Output Sets

Author

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  • Simeon Reich

    (The Technion – Israel Institute of Technology)

  • Truong Minh Tuyen

    (Thai Nguyen University of Sciences)

Abstract

We study the split common fixed point problem for Bregman relatively nonexpansive operators and the split feasibility problem with multiple output sets in real reflexive Banach spaces. Using Bregman distances, we propose several new cyclic projection algorithms for solving these problems.

Suggested Citation

  • Simeon Reich & Truong Minh Tuyen, 2021. "Projection Algorithms for Solving the Split Feasibility Problem with Multiple Output Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 861-878, September.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01910-2
    DOI: 10.1007/s10957-021-01910-2
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    References listed on IDEAS

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    1. Simeon Reich & Truong Minh Tuyen & Mai Thi Ngoc Ha, 2021. "An optimization approach to solving the split feasibility problem in Hilbert spaces," Journal of Global Optimization, Springer, vol. 79(4), pages 837-852, April.
    2. Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 301-316, Springer.
    3. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
    4. Simeon Reich & Truong Minh Tuyen, 2020. "Two Projection Algorithms for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 148-168, July.
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    Cited by:

    1. Aragón-Artacho, Francisco J. & Censor, Yair & Gibali, Aviv & Torregrosa-Belén, David, 2023. "The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning," Applied Mathematics and Computation, Elsevier, vol. 440(C).

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