Modified subgradient extragradient method for system of variational inclusion problem and finite family of variational inequalities problem in real Hilbert space

Journal of inequalities and applications

Atid Kangtunyakarn¹  Araya Kheawborisut¹ 

[1] Department of Mathematics, King Mongkut’s Institute of Technology Ladkrabang, 10520, Bangkok, Thailand;

关键词: System of variational inclusions problem;    Variational inequalities problem;    Half-space;    Nonexpansive mapping;   

DOI  :  10.1186/s13660-021-02583-1

来源: Springer

【 摘 要 】

For the purpose of this article, we introduce a modified form of a generalized system of variational inclusions, called the generalized system of modified variational inclusion problems (GSMVIP). This problem reduces to the classical variational inclusion and variational inequalities problems. Motivated by several recent results related to the subgradient extragradient method, we propose a new subgradient extragradient method for finding a common element of the set of solutions of GSMVIP and the set of a finite family of variational inequalities problems. Under suitable assumptions, strong convergence theorems have been proved in the framework of a Hilbert space. In addition, some numerical results indicate that the proposed method is effective.

【 授权许可】

CC BY