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

Seifu Endris Yimer, Poom Kumam, Anteneh Getachew Gebrie and Rabian Wangkeeree
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Seifu Endris Yimer: KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Poom Kumam: KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Anteneh Getachew Gebrie: Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, P.O. Box 445, Debre Berhan, Ethiopia
Rabian Wangkeeree: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Mathematics, 2019, vol. 7, issue 9, 1-21

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.

Keywords: minimization problem; fixed point problem; inertial term; bilevel variational inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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