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Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

Author

Listed:
  • Lu-Chuan Ceng

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
    These authors contributed equally to this work.)

  • Qing Yuan

    (School of Mathematics and Statistics, Linyi University, Linyi 276000, China
    These authors contributed equally to this work.)

Abstract

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

Suggested Citation

  • Lu-Chuan Ceng & Qing Yuan, 2019. "Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems," Mathematics, MDPI, vol. 7(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:123-:d:200621
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    References listed on IDEAS

    as
    1. Hideaki Iiduka, 2011. "Iterative Algorithm for Solving Triple-Hierarchical Constrained Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 580-592, March.
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