Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces. (18th August 2018)

• Record Type: Journal Article
• Authors: Tang, Guo-ji; Wan, Zhongping; Huang, Nan-jing
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 11(2018)
• Page Start: 1103
• Page End: 1119
• Publication Date: 2018-08-18
• Subjects: Extragradient method -- f-pseudomonotonicity -- mixed variational inequality; 49J40 -- 47J25 -- 47H05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1465952
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, a projection-type method for mixed variational inequalities is proposed in Hilbert spaces. The proposed method has the following nice features: (i) The algorithm is well defined whether the solution set of the problem is nonempty or not, under some mild assumptions; (ii) If the solution set is nonempty, then the sequence generated by the method is strongly convergent to the solution, which is closest to the initial point; (iii) The existence of the solutions to variational inequalities can be verified through the behavior of the generated sequence. The results presented in this article generalize and improve some known results.