A vector auxiliary principle technique approach to systems of mixed vector equilibrium problems. (1st February 2020)

• Record Type: Journal Article
• Authors: Chadli, Ouayl; Saidi, Asma; Zhao, Xiaopeng
• Is Part Of: Optimization. Volume 69:Number 2(2020)
• Page Start: 221
• Page End: 241
• Publication Date: 2020-02-01
• Subjects: mixed vector equilibrium problems -- vector auxiliary principle -- set-valued variational inequalities -- C-convex functions -- C-upper (lower) semicontinuity; 90C30 -- 90C29 -- 90C33 -- 49J40 -- 47J20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1553973
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we introduce and study a system of generalized mixed vector equilibrium problems involving set-valued variational-like inequalities (SGMVEP, in short) in the general setting of Banach spaces. First, we construct an associated vector auxiliary problem and establish existence results for it. This leads to the generation of an iterative algorithm for solving SGMVEP. Then, under weaker assumptions, the strong convergence of the proposed algorithm is established. The method adopted here is based on the vector auxiliary principle and the obtained results improve some existing results in the literature.