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Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces

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Abstract

In this paper, we consider a variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping called triple hierarchical variational inequality. We propose two iterative methods, one is implicit and another one is explicit, to compute the approximate solutions of our problem. We present an example of our problem. The convergence analysis of the sequences generated by the proposed methods is also studied.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lu-Chuan Ceng

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China

    Lu-Chuan Ceng

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  4. Center for General Education, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan

    Jen-Chih Yao

Authors
  1. Lu-Chuan Ceng
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  2. Qamrul Hasan Ansari
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  3. Jen-Chih Yao
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Correspondence to Qamrul Hasan Ansari or Jen-Chih Yao.

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Ceng, LC., Ansari, Q.H. & Yao, JC. Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces. J Optim Theory Appl 151, 489–512 (2011). https://doi.org/10.1007/s10957-011-9882-7

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  • DOI: https://doi.org/10.1007/s10957-011-9882-7

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