一类新的二阶切导数及其在集值优化中的应用  

A New Class of Second-order Tangent Derivatives with Applications to Set-valued Optimization

作　　者：徐义红[1] 王磊 XU YIHONG;WANG LEI(Department of Mathematics,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《应用数学学报》2020年第3期609-619,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11961047);江西省自然科学基金(20192BAB201010)资助项目。

摘　　要：提出了一种新的二阶切锥,讨论了它与二阶广义相依切集的关系.利用此锥定义了一种新的二阶切导数,讨论了它与二阶广义相依上图切导数的关系.利用Henig扩张锥的性质,给出了集值优化在Henig有效元意义下的二阶最优性必要条件.在近似锥-次类凸假设下给出了Benson真有效元意义下的二阶最优性必要条件.举例说明了本文的主要结论.A new class of second-order tangent cones is introduced,its relationship to the generalized second-order contingent set is discussed.With this cone,a new kind of secondorder tangent derivatives for set-valued maps is introduced,whose relationship to the generalized second-order contingent epiderivative is investigated.By applying properties of Henig dilating cone,a second-order necessary optimality condition for set-valued optimization is established in the sense of Henig efficient elements.Under near cone-subconvexlikeness assumption,a necessary optimality condition is also obtained in the sense of Benson properly efficient elements.Examples are given to illustrate the main results.

关 键 词：二阶切锥 广义二阶切导数 Henig有效元 Benson真有效元 

分 类 号：O221.6[理学—运筹学与控制论]