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Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

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  • Zhao-Rong Kong
  • Lu-Chuan Ceng
  • Qamrul Hasan Ansari
  • Chin-Tzong Pang

Abstract

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

Suggested Citation

  • Zhao-Rong Kong & Lu-Chuan Ceng & Qamrul Hasan Ansari & Chin-Tzong Pang, 2013. "Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, April.
    • Handle: RePEc:hin:jnlaaa:718624
    DOI: 10.1155/2013/718624
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