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The Strong Convergence of Douglas-Rachford Methods for the Split Feasibility Problem

In: Mathematical Analysis in Interdisciplinary Research

Author

Listed:
  • Qiao-Li Dong

    (College of Science, Civil Aviation University of China)

  • Lulu Liu

    (College of Science, Civil Aviation University of China)

  • Themistocles M. Rassias

    (National Technical University of Athens)

Abstract

In this article, we introduce several Douglas-Rachford method to solve the split feasibility problems (SFP). Firstly, we propose a new iterative method by combining Douglas-Rachford method and Halpern iteration. The stepsize is determined dynamically which does not need any prior information about the operator norm. A relaxed version is presented for the SFP where the two closed convex sets are both level sets of convex functions. The strong convergence of two proposed methods is established under standard assumptions. We also propose an iterative method by combining Douglas-Rachford method with Haugazeau algorithm, and show its strong convergence. The numerical examples are presented to illustrate the advantage of our methods by comparing with other methods.

Suggested Citation

  • Qiao-Li Dong & Lulu Liu & Themistocles M. Rassias, 2021. "The Strong Convergence of Douglas-Rachford Methods for the Split Feasibility Problem," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 213-233, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84721-0_12
    DOI: 10.1007/978-3-030-84721-0_12
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