Regularized hybrid iterative algorithms for triple hierarchical variational inequalities

Lu-Chuan Ceng Ngai-Ching Wong Jen-Chih Yao

Functional Analysis mathscidoc:1910.43724

Journal of Inequalities and Applications, 2014, (1), 490, 2014.12
In this paper, we introduce and study a triple hierarchical variational inequality (THVI) with constraints of minimization and equilibrium problems. More precisely, let Fix ( T ) be the fixed point set of a nonexpansive mapping, let Fix ( T ) be the solution set of a mixed equilibrium problem (MEP), and let <i></i> be the solution set of a minimization problem (MP) for a convex and continuously Frechet differential functional in Hilbert spaces. We want to find a solution Fix ( T ) of a variational inequality with a variational inequality constraint over the intersection of Fix ( T ) , Fix ( T ) , and <i></i>. We propose a hybrid iterative algorithm with regularization to compute approximate solutions of the THVI, and we present the convergence analysis of the proposed iterative algorithm.
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@inproceedings{lu-chuan2014regularized,
  title={Regularized hybrid iterative algorithms for triple hierarchical variational inequalities},
  author={Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020212004855908253},
  booktitle={Journal of Inequalities and Applications},
  volume={2014},
  number={1},
  pages={490},
  year={2014},
}
Lu-Chuan Ceng, Ngai-Ching Wong, and Jen-Chih Yao. Regularized hybrid iterative algorithms for triple hierarchical variational inequalities. 2014. Vol. 2014. In Journal of Inequalities and Applications. pp.490. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020212004855908253.
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