Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epiderivative  

作　　者：Zhi-ang ZHOU Xin-min YANG Qiu-sheng QIU 

机构地区：[1]College of Sciences, Chongqing University of Technology, Chongqing 400054, China [2]College of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China [3]Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第1期11-18,共8页应用数学学报（英文版）

基　　金：supported by the National Nature Science Foundation of China(11431004,11471291);the General Project of Chongqing Frontier and Applied Foundation Research(cstc2015jcyj A00050);the Key Project of Chongqing Frontier and Applied Foundation Research(cstc2017jcyj BX0055,cstc2015jcyj BX0113)

摘　　要：In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.

关 键 词：set-valued maps generalized cone convexity Henig proper efficiency contingent epiderivative optimality conditions 

分 类 号：O1[理学—数学]