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

被引：8
|
作者：
Yimer, Seifu Endris [1 ,2 ,3 ]
Kumam, Poom [1 ,2 ,4 ]
Gebrie, Anteneh Getachew [3 ]
Wangkeeree, Rabian [5 ]
机构：
[1] King Mongkuts Univ Technol Thonburi, Fac Sci, SCL Fixed Point Lab 802, KMUTTFixed Point Res Lab, 126 Pracha Uthit Rd, Bangkok 10140, Thailand
[2] King Mongkuts Univ Technol Thonburi, Fac Sci, Dept Math, 126 Pracha Uthit Rd, Bangkok 10140, Thailand
[3] Debre Berhan Univ, Coll Computat & Nat Sci, Dept Math, POB 445, Debre Berhan, Ethiopia
[4] King Mongkuts Univ Technol Thonburi, Ctr Excellence Theoret & Computat Sci TaCS CoE, Fac Sci, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand
[5] Naresuan Univ, Fac Sci, Dept Math, Phitsanulok 65000, Thailand
来源：
MATHEMATICS | 2019年 / 7卷 / 09期
关键词：
minimization problem; fixed point problem; inertial term; bilevel variational inequality; EXTRAGRADIENT ALGORITHM; ITERATIVE ALGORITHMS; STRONG-CONVERGENCE;
D O I：
10.3390/math7090841
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页数：21
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