改进集映射下参数广义向量拟平衡问题解映射的Berge下半连续性  

Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings

作　　者：邵重阳 彭再云 刘芙萍 王泾晶 SHAO Chongyang;PENG Zaiyun;LIU Fuping;WANG Jingjing(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,P.R.China;School of Mathematical Sciences,Chongqing Normal University,Chongqing 400047,P.R.China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074 [2]重庆师范大学数学科学学院,重庆400047

出　　处：《应用数学和力学》2020年第8期912-920,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11301571);重庆市巴渝学者计划;重庆市基础与前沿研究项目(cstc2018jcyjAX0337);重庆市留学归国人员创新项目(cx2019148);重庆市研究生教育创新基金(CYS20290)。

摘　　要：该文主要讨论了一类新的参数广义向量拟平衡问题解映射的稳定性.首先,定义了改进集映射,基于改进集映射,将序结构进行推广并应用于拟平衡问题的研究,得到了改进集映射下参数广义向量拟平衡问题(IPGVQEP).然后,给出了一类与改进集映射相关的非线性标量化函数Ψ,利用非线性标量化函数Ψ得到了与原问题(IPGVQEP)对应的标量化问题(IPGVQEP)Ψ,并获得了原问题与标量化问题解之间的关系.最后,引入了一个关键假设HΨ,借助关键假设HΨ及原问题与标量化问题间解的关系,获得了IPGVQEP解映射Berge下半连续性的充分必要条件,并举例验证了所得结果.The Berge lower semi-continuity of solution mapping for a new class of parametric generalized vector quasi-equilibrium problems was discussed.Firstly,the improvement set mapping was defined,based on which the order structure was generalized and applied to the study of vector quasi-equilibrium problems,to lead to parametric generalized vector quasi-equilibrium problems under improvement set mappings(IPGVQEP).Then,a nonlinear scalarization functionΨassociated with the improvement set mapping was introduced,the scalar problem(IPGVQEP)Ψcorresponding to the above problem(IPGVQEP)was given,and the relation between solution sets of IPGVQEP and(IPGVQEP)Ψwas obtained.Finally,by virtue of a key hypothesis HΨand the relation between solution sets,the sufficient and necessary conditions for Berge lower semi-continuity of the solution mapping for IPGVQEP were established,and an example was given to verify the results.

关 键 词：改进集映射 参数广义向量拟平衡问题 解映射 Berge下半连续性 标量化问题 

分 类 号：O224[理学—运筹学与控制论]