A Regularized Generalized Popov’s Method to Solve the Hierarchical Variational Inequality Problem with Generalized Lipschitzian Mappings

Symmetry

Yuanheng Wang¹  Bingnan Jiang¹  Yidan Gao¹ 

[1] College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;

关键词: generalized Lipschitzian mapping;    hierarchical variational inequality problem;    hemicontinuous mapping;    multi-step inertial iteration;    regularized generalized Popov’s method;   

DOI  :  10.3390/sym14020187

来源: DOAJ

【 摘 要 】

In this article, we introduce a new inertial multi-step regularized generalized Popov’s extra-gradient method to solve the hierarchical variational inequality problem (HVIP). We extend the previous Lipschitzian and strongly monotone mapping to a hemicontinuous, generalized Lipschitzian and strongly monotone mapping. We also obtain a strong convergence theorem about the new Popov’s algorithm. Furthermore, we utilize some numerical experiments to highlight the feasibility and effectiveness of our method.

【 授权许可】

Unknown