A Self-Adaptive Step Size Algorithm for Solving Variational Inequalities with the Split Feasibility Problem with Multiple Output Sets Constraints. (4th July 2022)

• Record Type: Journal Article
• Authors: Cuong, Tran Luu; Anh, Tran Viet; Van, Le Huynh My
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 9(2022)
• Page Start: 1009
• Page End: 1026
• Publication Date: 2022-07-04
• Subjects: Variational inequality -- split feasibility problem with multiple output sets -- self-adaptive -- strong convergence; 49J40 -- 90C33 -- 47H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2071939
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The strong convergence of the proposed algorithm is proved without knowing any information of the Lipschitz and strongly monotone constants of the mapping. In addition, the implementation of the algorithm does not require the computation or estimation of the norms of the given bounded linear operators. Special cases are considered. Finally, a numerical experiment has been carried out to illustrate the proposed algorithm.