关于含参可行集映射的下半连续性的一个记注  

A Note on the Lower Semicontinuity of Parameter-Containing Feasible Set Mappings

作　　者：李高西 李季 杨洁[2] LI Gao-xi;LI Ji;YANG Jie(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;School of Finance and Economics,Chongqing City Management College,Chongqing 401331,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆城市管理职业学院财经学院,重庆401331 [3]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《西南大学学报（自然科学版）》2020年第7期139-142,共4页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11901068);重庆市自然科学基金面上项目(cstc2019jcyj-msxmX0456);重庆市教委科研项目(KJQN201800810);重庆工商大学高层次人才科研启动项目(1856009,1756006).

摘　　要：讨论了含参可行集映射在分别满足Cottle,Abadie,Guignard和Constraint Rank(CR)约束规范时的下半连续性.给出了在满足Cottle约束规范时的下半连续性定理,并通过反例证明了该含参可行集映射在Abadie,Guignard和CR这3种约束规范下不一定具有下半连续性,这些结论可用于非线性规划和半无限规划.This paper studies the lower semicontinuity of parameter-containing feasible set mappings for inequality constraints under some constraint qualifications(CQ)such as Cottle's CQ,Abadie's CQ,Guignard's CQ and CRCQ.We obtain thetheorem oflower semicontinuity of this parameter-containing feasible set mapping under Cottle's CQ.A counter-example is given to show that the lower semicontinuity of this parameter-containing feasible set mapping cannot be obtained under Abadie's CQ,Guignard's CQ or CRCQ.These results may be usedin dealing withnonlinear programming and semi-infinite programming problems.

关 键 词：非线性规划 下半连续性 可行集映射 约束规范 

分 类 号：O224[理学—运筹学与控制论]