Three novel inertial explicit Tseng's extragradient methods for solving pseudomonotone variational inequalities. (16th December 2022)

• Record Type: Journal Article
• Authors: ur Rehman, Habib; Kumam, Poom; Ozdemir, Murat; Argyros, Ioannis K.; Kumam, Wiyada
• Is Part Of: Optimization. Volume 71:Number 16(2022)
• Page Start: 4697
• Page End: 4730
• Publication Date: 2022-12-16
• Subjects: Variational inequalities -- Tseng's extragradient method -- inertial methods -- pseudomonotone mapping -- strong convergence theorem; 65Y05 -- 65K15 -- 68W10 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1963248
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we construct three new extragradient-type iterative methods for solving variational inequalities in real Hilbert spaces. The proposed iterative methods are functionally equivalent to the extragradient method, which is used to solve variational inequalities in an infinite-dimensional real Hilbert space. The main advantage of these iterative methods is that they use a simple step size rule based on operator information instead of the Lipschitz constant or any line search method. Three strong convergence theorems are well proved, corresponding to the proposed methods by allowing certain control parameter conditions. Finally, we present some numerical experiments to verify the efficacy and superiority of the proposed iterative methods.