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Optimization Letters

, Volume 12, Issue 1, pp 87–102 | Cite as

Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings

  • Q. L. Dong
  • H. B. Yuan
  • Y. J. Cho
  • Th. M. Rassias
Original Paper

Abstract

In this article, we first introduce a modified inertial Mann algorithm and an inertial CQ-algorithm by combining the accelerated Mann algorithm and the CQ-algorithm with the inertial extrapolation, respectively. This strategy is intended to speed up the convergence of the given algorithms. Then we established the convergence theorems for two provided algorithms. For the inertial CQ-algorithm, the conditions on the inertial parameters are very weak. Finally, the numerical experiments are presented to illustrate that the modified inertial Mann algorithm and inertial CQ-algorithm may have a number of advantages over other methods in computing for some cases.

Keywords

Nonexpansive mapping Inertial extrapolation CQ-algorithm The inertial Mann algorithm Mann algorithm The accelerated Mann algorithm 

Notes

Acknowledgements

Supported by National Natural Science Foundation of China (No. 61379102) and Open Fund of Tianjin Key Lab for Advanced Signal Processing (No. 2016ASP-TJ01). Also, the third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning (2014R1A2A2A01002100). The authors would like to thank three anonymous referees for their careful reading of an earlier version of this paper and constructive suggestions. In particular, one referee gave us very valuable comments on the numerical experiments, which enabled us to improve the paper greatly.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Q. L. Dong
    • 1
    • 2
  • H. B. Yuan
    • 1
  • Y. J. Cho
    • 3
    • 4
  • Th. M. Rassias
    • 5
  1. 1.College of ScienceCivil Aviation University of ChinaTianjinChina
  2. 2.Tianjin Key Lab for Advanced Signal ProcessingCivil Aviation University of ChinaTianjinChina
  3. 3.Department of Mathematics Education and RINSGyeongsang National UniversityJinjuKorea
  4. 4.Center for General EducationChina Medical UniversityTaichungTaiwan
  5. 5.Department of MathematicsNational Technical University of AthensAthensGreece

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