A subgradient extragradient algorithm for solving monotone variational inequalities in Banach spaces

Journal of Inequalities and Applications

Fei Ma¹ 

[1] School of Mathematics and Information Science, Xianyang Normal University;

关键词: Variational inequalities;    Subgradient extragradient method;    Monotone mapping;    Convex set;    Strong convergence;   

DOI  :  10.1186/s13660-020-2295-0

来源: DOAJ

【 摘 要 】

Abstract In this paper, we introduce an algorithm for solving classical variational inequalities problem with Lipschitz continuous and monotone mapping in Banach space. We modify the subgradient extragradient methods with a new and simple iterative step size, the strong convergence of algorithm is established without the knowledge of the Lipschitz constant of the mapping. Finally, a numerical experiment is presented to show the efficiency and advantage of the proposed algorithm. Our results generalize some of the work in Hilbert spaces to Banach spaces.

【 授权许可】

Unknown