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General Inertial Mann Algorithms and Their Convergence Analysis for Nonexpansive Mappings

In: Applications of Nonlinear Analysis

Author

Listed:
  • Qiao-Li Dong

    (College of Science, Civil Aviation University of China)

  • Yeol Je Cho

    (Gyeongsang National University
    China Medical University)

  • Themistocles M. Rassias

    (National Technical University of Athens)

Abstract

In this article, we introduce general inertial Mann algorithms for finding fixed points of nonexpansive mappings in Hilbert spaces, which includes some other algorithms as special cases. We reanalyze the accelerated Mann algorithm, which actually is an inertial type Mann algorithm. We investigate the convergence of the general inertial Mann algorithm, based on which, the strict convergence condition on the accelerated Mann algorithm is eliminated. Also, we apply the general inertial Mann algorithm to show the existence of solutions of the minimization problems by proposing a general inertial type gradient-projection algorithm. Finally, we give preliminary experiments to illustrate the advantage of the accelerated Mann algorithm.

Suggested Citation

  • Qiao-Li Dong & Yeol Je Cho & Themistocles M. Rassias, 2018. "General Inertial Mann Algorithms and Their Convergence Analysis for Nonexpansive Mappings," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Applications of Nonlinear Analysis, pages 175-191, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-89815-5_7
    DOI: 10.1007/978-3-319-89815-5_7
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