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Mildly Inertial Subgradient Extragradient Method for Variational Inequalities Involving an Asymptotically Nonexpansive and Finitely Many Nonexpansive Mappings

Author

Listed:
  • Lu-Chuan Ceng

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

  • Xiaolong Qin

    (General Education Center, National Yunlin University of Science and Technology, Douliou 64002, Taiwan)

  • Yekini Shehu

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, Taichung 40447, Taiwan)

Abstract

In a real Hilbert space, let the notation VIP indicate a variational inequality problem for a Lipschitzian, pseudomonotone operator, and let CFPP denote a common fixed-point problem of an asymptotically nonexpansive mapping and finitely many nonexpansive mappings. This paper introduces mildly inertial algorithms with linesearch process for finding a common solution of the VIP and the CFPP by using a subgradient approach. These fully absorb hybrid steepest-descent ideas, viscosity iteration ideas, and composite Mann-type iterative ideas. With suitable conditions on real parameters, it is shown that the sequences generated our algorithms converge to a common solution in norm, which is a unique solution of a hierarchical variational inequality (HVI).

Suggested Citation

  • Lu-Chuan Ceng & Xiaolong Qin & Yekini Shehu & Jen-Chih Yao, 2019. "Mildly Inertial Subgradient Extragradient Method for Variational Inequalities Involving an Asymptotically Nonexpansive and Finitely Many Nonexpansive Mappings," Mathematics, MDPI, vol. 7(10), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:881-:d:269630
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    References listed on IDEAS

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