自由支配集下近似平衡约束向量优化问题的稳定性研究  

Stability of Vector Optimization Problems Under Approximate Equilibrium Constraints via Free-Disposal Sets

作　　者：曾悦 彭再云 梁仁莉 邵重阳 ZENG Yue;PENG Zaiyun;LIANG Renli;SHAO Chongyang(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,P.R.China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《应用数学和力学》2021年第9期958-967,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11301571);重庆市基础与前沿研究项目(cstc2018jcyjAX0337);重庆市巴渝学者计划;重庆市研究生导师团队建设项目(JDDSTD201802);重庆市研究生教育创新基金(CYS20290);重庆市高校创新研究群体项目(CXQT21021);最优化与控制教育部重点实验室开放基金重点课题(CSSXKFKTZ201801)。

摘　　要：在自由支配集下,对一类近似平衡约束向量优化问题(AOPVF)的稳定性进行研究.首先,在较弱的凸性假设下获得了约束集映射的Berge-半连续性和约束集的闭性、凸性和紧性结果.然后,在目标函数列Gamma-收敛的假设下,分别得到了AOPVF弱有效解映射Berge-半连续和弱有效解集下Painlevé-Kuratowski收敛的充分条件,并给出例子说明结论是新颖和有意义的.The stability of vector optimization problems under approximate equilibrium constraints(AOPVF)via free-disposal sets was discussed.Firstly,the Berge-semicontinuity of the constraint set mapping and the closedness,the convexity and the compactness of the constraint set were obtained with the weaker convexity assumption.Moreover,under the assumption of Gamma-convergence for the objective functional sequences,the lower Painlevé-Kuratowski convergence of the weak efficient solution set and the Berge-semicontinuity of weak efficient solution mappings for AOPVF were obtained respectively.Some examples illustrate that the results are new and meaningful.

关 键 词：自由支配集 Gamma-收敛 Berge-半连续 下Painlevé-Kuratowski收敛 

分 类 号：O224[理学—运筹学与控制论]