Viscosity Approximation Methods for a Class of Generalized Split Feasibility Problems with Variational Inequalities in Hilbert Space. (11th June 2019)

• Record Type: Journal Article
• Authors: Tian, Ming; Jiang, Bing-Nan
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 8(2019)
• Page Start: 902
• Page End: 923
• Publication Date: 2019-06-11
• Subjects: Iterative algorithms -- split feasibility problems -- Strong convergence -- variational inequalities -- viscosity approximation; 58E35 -- 47H09 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1564763
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP's with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space.