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Linear Convergence of an Iterative Algorithm for Solving the Multiple-Sets Split Feasibility Problem

Author

Listed:
  • Tingting Tian

    (Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China)

  • Luoyi Shi

    (Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China)

  • Rudong Chen

    (Department of Mathematical Science, Tianjin Polytechnic University, Tianjin 300387, China)

Abstract

In this paper, we propose the simultaneous sub-gradient projection algorithm with the dynamic step size (SSPA for short) for solving the multiple-sets split feasibility problem (MSSFP for short) and investigate its linear convergence. We involve a notion of bounded linear regularity for the MSSFP and construct several sufficient conditions to prove the linear convergence for the SSPA. In particular, the SSPA is an easily calculated algorithm that uses orthogonal projection onto half-spaces. Furthermore, some numerical results are provided to verify the effectiveness of our proposed algorithm.

Suggested Citation

  • Tingting Tian & Luoyi Shi & Rudong Chen, 2019. "Linear Convergence of an Iterative Algorithm for Solving the Multiple-Sets Split Feasibility Problem," Mathematics, MDPI, vol. 7(7), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:644-:d:249658
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