Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications. (2nd January 2021)

• Record Type: Journal Article
• Authors: Su, Tran Van; Hien, Nguyen Duc
• Is Part Of: Optimization. Volume 70:Number 1(2021)
• Page Start: 121
• Page End: 148
• Publication Date: 2021-01-02
• Subjects: Higher-order necessary and sufficient efficiency conditions for constrained vector equilibrium problems -- local weak efficient solutions -- higher-order Studniarski's derivatives -- contingent cones; 90C46 -- 91B50 -- 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1702985
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This article is devoted to the investigation of a vector equilibrium problem involving equality, inequality and set constraints with nonsmooth functions via the higher-order Studniarski derivatives. Under the suitable constraint qualifications, higher-order Karush-Kuhn-Tucker type necessary efficiency conditions for the local weak efficient solutions of a constrained vector equilibrium problem are given. Under suitable assumptions on the objective and constraint functions, the higher-order Karush-Kuhn-Tucker type necessary optimality conditions for local weak efficient solutions become the sufficient conditions. As applications, we obtain the first-order and higher-order optimality conditions for the local weak efficient solutions of a constrained vector variational inequality problem, a constrained vector optimization problem and a transportation problem with two-sided constraints on supplies or demands in terms of Studniarski's derivatives. Several examples are also provided to illustrate the results of the paper.