Inertial subgradient extragradient method for solving pseudomonotone variational inequality problems in Banach spaces

Abstract

In this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures.

Keywords:

• Variational inequalities
• pseudomonotone operator
• Banach space
• subgradient extragradient method
• strong convergence

Mathematics Subject Classifications:

• 47H05
• 47H07
• 47H10
• 54H25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was supported by the National Natural Science Foundation of China (12271067), the Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0080), the Group Building Project for Scientific Innovation for Universities in Chongqing (CXQT21021) and the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K202200704). The second author was supported by the Chongqing Jiaotong University Postgraduate Research Innovation Project (2022S0070) and the Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016). The third author supported by the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1318). The fourth author supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000710), the Chongqing Natural Science Foundation (CSTB2022NSCQ-MSX1498).