Mathematics (Sep 2019)

Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints

  • Seifu Endris Yimer,
  • Poom Kumam,
  • Anteneh Getachew Gebrie,
  • Rabian Wangkeeree

DOI
https://doi.org/10.3390/math7090841
Journal volume & issue
Vol. 7, no. 9
p. 841

Abstract

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In this paper, we introduce an iterative scheme with inertial effect using Mann iterative scheme and gradient-projection for solving the bilevel variational inequality problem over the intersection of the set of common fixed points of a finite number of nonexpansive mappings and the set of solution points of the constrained optimization problem. Under some mild conditions we obtain strong convergence of the proposed algorithm. Two examples of the proposed bilevel variational inequality problem are also shown through numerical results.

Keywords