A projection-fixed point method for a class of bilevel variational inequalities with split fixed point constraints. (2nd June 2016)

• Record Type: Journal Article
• Authors: Anh, Tran Viet; Muu, Le Dung
• Is Part Of: Optimization. Volume 65:Number 6(2016)
• Page Start: 1229
• Page End: 1243
• Publication Date: 2016-06-02
• Subjects: split feasibility problem -- bilevel variational inequality -- Krasnoselskii–Mann scheme -- projection method -- nonexpansive mapping; 47J25 -- 47N10 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1101599
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We propose a method for solving bilevel split variational inequalities involving strongly monotone operators in the leader problems and nonexpansive mappings in the follower ones. The proposed method is a combination between the projection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. Strong convergence of the iterative process is proved. Special cases are considered.