Inertial method for bilevel variational inequality problems with fixed point and minimizer point constraints
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Author list: Yimer S.E., Kumam P., Gebrie A.G., Wangkeeree R.
Publisher: MDPI
Publication year: 2019
Journal: Mathematics (2227-7390)
Volume number: 7
Issue number: 9
ISSN: 2227-7390
eISSN: 2227-7390
Languages: English-Great Britain (EN-GB)
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Abstract
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. ฉ 2019 by the authors.
Keywords
Bilevel variational inequality, Inertial term, Minimization problem
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