On second-order optimality conditions for continuously Fréchet differentiable vector optimization problems. (2nd December 2018)

• Record Type: Journal Article
• Authors: Feng, Min; Li, Shengjie
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2117
• Page End: 2137
• Publication Date: 2018-12-02
• Subjects: Vector optimization -- Karush–Kuhn–Tucker conditions -- constraint qualifications -- second-order optimality conditions; 26A24 -- 49K99 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1545122
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we study a vector optimization problem (VOP) with both inequality and equality constraints. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point of study. By virtue of a second-order constraint qualification of Abadie type, we provide second-order Karush–Kuhn–Tucker type necessary optimality conditions for the VOP. Moreover, we also obtain second-order sufficient optimality conditions for a kind of strict local efficiency. Both the necessary conditions and the sufficient conditions are shown in equivalent pairs of primal and dual formulations by using theorems of the alternative for the VOP.