一类新的二阶组合切导数及其应用  

A new kind of second-order composed tangent derivatives and its applications

作　　者：周丽霞 徐义红[1] 吕强[1] ZHOU Lixia1 XU Yihong1 LU Qiang1

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《运筹学学报》2017年第3期45-54,共10页Operations Research Transactions

基　　金：国家自然科学基金(No.11461044);江西省自然科学基金(No.20151BAB 201027);江西省教育厅科技项目(No.GJJ12010)

摘　　要：引进了一种新的切锥,讨论它与相依切锥的关系.借助这种新的切锥引进了一类新的二阶组合切导数,并讨论了它与其他二阶切导数的关系.利用这类新的二阶组合切导数,建立了集值优化分别取得Henig有效元和全局有效元的最优性必要条件.A new kind of tangent cones is introduced, whose relationship to the contingent cone is discussed. With the introduced cones, a new kind of second-order tangent derivatives, termed second-order composed tangent derivatives, is developed, and its relationship to other second-order composed tangent derivatives is discussed. Then, with the help of second-order composed tangent derivatives, optimality necessary conditions are established respectively for a Henig efficient solution and a globally proper efficient solution of set-valued optimization.

关 键 词：切锥 二阶组合切导数 Henig有效元 全局有效元 

分 类 号：O221.6[理学—运筹学与控制论]