Accelerated hybrid and shrinking projection methods for variational inequality problems. (4th May 2019)

• Record Type: Journal Article
• Authors: Duong Viet, Thong; Vinh, Nguyen The; Van Hieu, Dang
• Is Part Of: Optimization. Volume 68:Number 5(2019)
• Page Start: 981
• Page End: 998
• Publication Date: 2019-05-04
• Subjects: Variational inequality problem -- subgradient extragradient method -- inertial method -- Tseng's extragradient method -- hybrid projection method -- shrinking projection method; 65Y05 -- 65K15 -- 68W10 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1566825
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we introduce several new extragradient-like approximation methods for solving variational inequalities in Hilbert spaces. Our algorithms are based on Tseng's extragradient method, subgradient extragradient method, inertial method, hybrid projection method and shrinking projection method. Strong convergence theorems are established under appropriate conditions. Our results extend and improve some related results in the literature. In addition, the efficiency of our algorithms is shown through numerical examples which are defined by the hybrid projection methods.