Second-order Optimality Conditions for Cone-subarcwise Connected Set-valued Optimization Problems  

作　　者：Zhen-hua PENG Yi-hong XU 

机构地区：[1]Department of Mathematics, Nanchang University

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第1期183-196,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China Grant 11461044;the Natural Science Foundation of Jiangxi Province(20151BAB201027);the Science and Technology Foundation of the Education Department of Jiangxi Province(GJJ12010)

摘　　要：The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.The concept of a cone subarcwise connected set-valued map is introduced. Several examples are given to illustrate that the cone subarcwise connected set-valued map is a proper generalization of the cone arcwise connected set-valued map, as well as the arcwise connected set is a proper generalization of the convex set,respectively. Then, by virtue of the generalized second-order contingent epiderivative, second-order necessary optimality conditions are established for a point pair to be a local global proper efficient element of set-valued optimization problems. When objective function is cone subarcwise connected, a second-order sufficient optimality condition is also obtained for a point pair to be a global proper efficient element of set-valued optimization problems.

关 键 词：cone subarcwise connected set-valued map generalized contingent epiderivative global proper efficiency optimality condition 

分 类 号：O1[理学—数学]