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Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem

Author

Listed:
  • Dianlu Tian

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Lining Jiang

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Luoyi Shi

    (Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China)

Abstract

The inverse problem is one of the four major problems in computational mathematics. There is an inverse problem in medical image reconstruction and radiotherapy that is called the multiple-sets split equality problem. The multiple-sets split equality problem is a unified form of the split feasibility problem, split equality problem, and split common fixed point problem. In this paper, we present two iterative algorithms for solving it. The suggested algorithms are based on the gradient method with a selection technique. Based on this technique, we only need to calculate one projection in each iteration.

Suggested Citation

  • Dianlu Tian & Lining Jiang & Luoyi Shi, 2019. "Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem," Mathematics, MDPI, vol. 7(10), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:928-:d:274066
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    References listed on IDEAS

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    1. Andrzej Cegielski, 2015. "General Method for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 385-404, May.
    2. Abdellatif Moudafi, 2013. "Alternating CQ-Algorithms For Convex Feasibility And Split Fixed-Point Problems," Documents de Travail 2013-02, CEREGMIA, Université des Antilles et de la Guyane.
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    Cited by:

    1. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

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