基于改进集的统一含参广义集值均衡问题解映射的下半连续性  

Lower semicontinuity of the solution maps of unified parametric generalized set-valued equilibrium problems with the improvement sets

作　　者：周志昂 陈望 余国林 Zhiang Zhou;Wang Chen;Guolin Yu

机构地区：[1]重庆理工大学理学院,重庆400054 [2]四川大学数学学院,成都610065 [3]北方民族大学数学与信息科学学院,银川750030

出　　处：《中国科学：数学》2023年第7期1025-1038,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12171061和11861002);重庆市教育委员会科学技术研究计划(批准号:KJZD-K202001104)资助项目。

摘　　要：本文研究含参广义集值均衡问题解映射的下半连续性.首先,利用改进集引进两类统一的含参广义集值均衡问题.其次,在合适的假设下,建立两类模型的标量化结果.最后,在新的假设下(不需要集值映射的单调性和解集的任何信息),用标量化方法研究本文提出的两类含参集值均衡问题解映射的下半连续性,并通过算例描述所获得的结果.In this paper,we investigate the lower semicontinuity of solution maps for parametric generalized set-valued equilibrium problems.Firstly,we introduce two classes of unified parametric generalized set-valued equilibrium problems via improvement sets.Secondly,we establish the scalarization results of two kinds of models under the suitable assumptions.Finally,based on the new assumptions,which do not use monotonicity of set-valued maps and any information about the solution sets,we investigate the lower semicontinuity of the solution maps for the proposed two kinds of parametric generalized set-valued equilibrium problems by using the scalarization method.Some examples are provided to illustrate the obtained results.

关 键 词：集值均衡问题 改进集 解映射 下半连续 标量化 

分 类 号：O224[理学—运筹学与控制论]