Inertial Haugazeau's hybrid subgradient extragradient algorithm for variational inequality problems in Banach spaces. (3rd June 2021)

• Record Type: Journal Article
• Authors: Tian, Ming; Jiang, Bing-Nan
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 987
• Page End: 1007
• Publication Date: 2021-06-03
• Subjects: Variational inequality problem -- extragradient algorithm -- inertial -- Banach space -- Haugazeau's hybrid method; 58E35 -- 47H09 -- 65J15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1731808
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The variational inequality problem plays an important role in nonlinear analysis and optimization. It is a generalization of the nonlinear complementarity problem. For a variational inequality problem in a Hilbert space, the extragradient algorithm with inertial effects has been studied. For a variational inequality problem in a Banach space, Nakajo introduced Haugazeau's hybrid method and Liu introduced the Halpern subgradient extragradient method. In this paper, we construct a new inertial iterative method for solving variational inequality problems in Banach spaces based on the work we mentioned above. We propose a strong convergence theorem. As applications, our result can be used to solve constrained convex minimization problems.