关于半无限优化问题稳定性的注记

Notes on Stability of Semi-Infinite Vector Optimization Problems

【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.