Higher-order Optimality Conditions and Duality for Approximate Solutions in Non-convex Set-valued Optimization  

作　　者：Guo-lin YU Tian-tian GONG 

机构地区：[1]North Minzu University

出　　处：《Acta Mathematicae Applicatae Sinica》2019年第3期620-628,共9页应用数学学报（英文版）

基　　金：supported by Natural Science Foundation of China government under Grant No.11861002;Natural Science Foundation of Ningxia under Grant No.NZ17112;First-Class Disciplines Foundation of Ningxia under Grant No.NXYLXK2017B09;The Key Project of North Minzu University under Grant No.ZDZX201804;Graduate Innovation Project of North Minzu University No.YCX19122;Nonlinear analysis and financial optimization research center of North Minzu University

摘　　要：This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps. Firstly, under the assumption of near cone-subconvexlikeness for set-valued maps, the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then, applications to Mond-Weir type dual problem are presented.

关 键 词：studniarski DERIVATIVES OPTIMALITY conditions SET-VALUED optimization problem efficiency DUALITY 

分 类 号：O1[理学—数学]