Tykhonov well-posedness for lexicographic equilibrium problems. (1st November 2016)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc; Duy, Tran Quoc
• Is Part Of: Optimization. Volume 65:Number 11(2016)
• Page Start: 1929
• Page End: 1948
• Publication Date: 2016-11-01
• Subjects: Lexicographic order -- equilibrium problems -- variational inequalities -- Tykhonov well-posedness; 49K40 -- 90C31 -- 91B50; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1209673
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider the vector equilibrium problems involving lexicographic cone in Banach spaces. We introduce the new concepts of the Tykhonov well-posedness for such problems. The corresponding concepts of the Tykhonov well-posedness in the generalized sense are also proposed and studied. Some metric characterizations of well-posedness for such problems are given. As an application of the main results, several results on well-posedness for the class of lexicographic variational inequalities are derived.