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Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem

Author

Listed:
  • Xinglong Wang

    (College of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China)

  • Jing Zhao

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Dingfang Hou

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

Abstract

The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

Suggested Citation

  • Xinglong Wang & Jing Zhao & Dingfang Hou, 2019. "Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem," Mathematics, MDPI, vol. 7(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:119-:d:200278
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    References listed on IDEAS

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    1. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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