A new self-adaptive algorithm for solving pseudomonotone variational inequality problems in Hilbert spaces. (2nd December 2022)

• Record Type: Journal Article
• Authors: Duong Viet, Thong; Van Long, Luong; Li, Xiao-Huan; Dong, Qiao-Li; Cho, Yeol Je; Tuan, Pham Anh
• Is Part Of: Optimization. Volume 71:Number 12(2022)
• Page Start: 3669
• Page End: 3693
• Publication Date: 2022-12-02
• Subjects: Subgradient extragradient method -- inertial method -- variational inequality problem -- pseudomonotone mapping -- Lipschitz continuity -- convergence rate; 65Y05 -- 65K15 -- 68W10 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1909584
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we revisit the subgradient extragradient method for solving a pseudomonotone variational inequality problem with the Lipschitz condition in real Hilbert spaces. A new algorithm based on the subgradient extragradient method with the technique of choosing a new step size is proposed. The weak convergence of the proposed algorithm is established under the pseudomonotonicity and the Lipschitz continuity as well as without using the sequentially weakly continuity of the variational inequality mapping and the nonasymptotic O ( 1 / n ) convergence rate of the proposed algorithm is presented, while the strong convergence theorem of the proposed algorithm is also proved under the strong pseudomonotonicity and the Lipschitz continuity hypotheses. In order to show the computational effectiveness of our algorithm, some numerical results are provided.