Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems

被引：1
作者：
Bing Tan
Xiaolong Qin
Jen-Chih Yao
机构：
[1] University of Electronic Science and Technology of China,Institute of Fundamental and Frontier Sciences
[2] Hangzhou Normal University,Department of Mathematics
[3] China Medical University,Research Center for Interneural Computing, China Medical University Hospital
[4] National Sun Yat-sen University,Department of Applied Mathematics
来源：
Numerical Algorithms | 2021年 / 88卷
关键词：
Bilevel variational inequality problem; Inertial extragradient method; Projection and contraction method; Hybrid steepest descent method; Pseudomonotone mapping; 47H05; 47J20; 47J25; 65Y05; 65K15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms are that they only need to calculate one projection on the feasible set in each iteration, and do not require the prior information of the Lipschitz constant of the cost operator. Furthermore, two new algorithms are derived to solve variational inequality problems. We establish the strong convergence of the proposed algorithms under some suitable conditions imposed on parameters. Finally, several numerical results and applications in optimal control problems are reported to illustrate the efficiency and advantages of the proposed algorithms.
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页码：1757 / 1786
页数：29
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