向量值映射的恰当锥拟凸性和锥半连续性的刻画  

Characterizations of Proper Cone Quasiconvexity and Cone Semicontinuity via Nonlinear Scalarization Functions for Vector-valued Maps

作　　者：李飞[1] 杨新民 LI FEI;YANG Xinmin(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Mathematical Sciences,Chongqing Normal University,Chongqing 400047,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]重庆师范大学数学科学学院,重庆400047

出　　处：《应用数学学报》2021年第5期646-658,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11601248,11431004)资助项目。

摘　　要：首先讨论了一个非线性标量化函数的基本性质并给出了其对偶形式.在此基础上建立了对向量值映射的恰当锥拟凸性的刻画.然后提出了锥形邻域的概念并给出了向量值映射的一类新的锥半连续性的统一定义.最后通过两个非线性标量化函数得到了对向量值映射的锥半连续性的完整刻画.In this paper,we firstly investigate some fundamental properties of a nonlinear scalarization function and also give its dual form.As an application,characterization of proper cone quasiconvexity for vector-valued maps is established.Then the concepts of cone-shaped neighborhoods and a new class of cone semicontinuity are introduced.Besides,by using two nonlinear scalarization functions,we have obtained complete and unified characterizations of cone semicontinuity for vector-valued maps.

关 键 词：非线性标量化函数 恰当锥拟凸性 锥形邻域 锥半连续性 锥连续性 

分 类 号：O221.6[理学—运筹学与控制论]