关于半无限优化问题稳定性的注记  

Notes on Stability of Semi-Infinite Vector Optimization Problems

作　　者：曾悦 彭再云 彭健益 文铭 ZENG Yue;PENG Zaiyun;PENG Jianyi;WEN Ming(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《重庆师范大学学报（自然科学版）》2022年第5期1-6,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(11301571);重庆市高校创新研究群体项目(No.CXQT21021);重庆市自然科学基金面上项目(No.cstc2021jcyjmsxmX0080);重庆市研究生联合培养基地建设项目(No.JDLHPYJD2021016);重庆交通大学校级研究生科研创新项目(No.2021S0061)。

摘　　要：【目的】对半无限向量优化问题约束集映射的稳定性进行研究。【方法】首先,举例说明Peng等人在2018年的一篇文献中的相关结论是有缺陷的。然后借助函数的自然拟C-凸性,分别获得了约束集映射的Berge-下半连续性和约束集的Painlevé-Kuratowski收敛性。【结果】基于函数的自然拟C-凸性,获得了约束集映射的稳定性结果。【结论】克服了原文献中相关定理的缺陷,并举例说明所得的新结论改进了相应结果。[Purposes]The stability for the constraint set mapping of semi-infinite vector optimization problems is discussed. [Methods]Firstly, examples are given to illustrate that the relevant conclusions of Peng’ paper in 2018 are defective. Then, by using the naturally quasiC-convexity of functions, Berge-lower semicontinuity of constraint set mappings and the Painlevé-Kuratowski convergence of constraint sets were obtained respectively. [Findings]Based on the naturally quasiC-convexity of functions, the stability of the constraint set mapping are obtained. [Conclusions]It overcomes the defect of the relevant theorems in former paper. Some examples illustrate that the new results improve the corresponding results.

关 键 词：半无限向量优化 Berge-下半连续 Painlevé-Kuratowski收敛 

分 类 号：O224[理学—运筹学与控制论]