On Optimality Conditions for Henig Efficiency and Superefficiency in Vector Equilibrium Problems. (10th December 2018)

• Record Type: Journal Article
• Authors: Luu, Do Van; Mai, Tran Thi
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 16(2018)
• Page Start: 1833
• Page End: 1854
• Publication Date: 2018-12-10
• Subjects: Clarke subdifferential -- local Henig efficient solutions -- local superefficient solutions -- Michel–Penot subdifferential -- vector equilibrium problems -- vector optimization problems -- vector variational inequalities; 90C46 -- 91B50 -- 49J52; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1501580
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Necessary optimality conditions for local Henig efficient and superefficient solutions of vector equilibrium problems involving equality, inequality, and set constraints in Banach space with locally Lipschitz functions are established under a suitable constraint qualification via the Michel–Penot subdifferentials. With assumptions on generalized convexity, necessary conditions for Henig efficiency and superefficiency become sufficient ones. Some applications to vector variational inequalities and vector optimization problems are given as well.