一种新的二阶次梯度及其在刻画集值优化弱有效元中的应用  

A New Kind of Second-Order Subgradient and Applications to the Characterizations for Weak Minimizer of Set-Valued Optimization Problem

作　　者：徐义红[1] 彭振华[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《应用数学学报》2017年第2期204-217,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(11461044);江西省自然科学基金項目(20151BAB201027);江西省教育厅科技项目(GJJIMIO)资助

摘　　要：引进了一种新的修正的二阶切锥,借助此切锥针对集值映射引进了一种新的二阶切导数,讨论了它的若干性质.利用此修正的二阶切导数,引进了一种新的在弱有效元意义下的二阶次梯度,并建立了它的一个存在性定理.借助此二阶次梯度给出了集值优化弱有效元的一种新刻画.A new kind of modified second-order tangent cone is introduced, with which a new kind of modified second-order tangent derivatives for a set-valued function is introduced, those properties are investigated. By using modified second-order tangent derivative, a new kind of second-order weakly efficient subgradients is introduced, whose existence theorem is established, in terms of which the characterizations of the weak minimizer of set-valued optimization problem are presented.

关 键 词：二阶次梯度 弱有效元 集值映射 锥 

分 类 号：O221.6[理学—运筹学与控制论]