On Hölder continuity of solution maps to parametric vector primal and dual equilibrium problems. (3rd August 2018)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc; Thanh Duoc, Pham; Tam, Tran Ngoc
• Is Part Of: Optimization. Volume 67:Number 8(2018)
• Page Start: 1169
• Page End: 1182
• Publication Date: 2018-08-03
• Subjects: Hölder continuity -- parametric vector equilibrium problem -- strong convexity -- vector optimization problem -- vector variational inequality; 49K40 -- 90C31 -- 91B50; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1466298
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we first propose some kinds of the strong convexity (concavity) for vector functions. Then we apply these assumptions to establish sufficient conditions for the Hölder continuity of solution maps of the vector primal and dual equilibrium problems in metric linear spaces. As applications, we derive the Hölder continuity of solution maps of vector optimization problems and vector variational inequalities. Our results improve and generalize some recent existing ones in the literature.