有限理性下集值优化问题的Levitin-Polyak良定性  

Levitin-Polyak Well-Posedness for Set-Valued Optimization Problems Under Bounded Rationality

作　　者：伍玉涛 贾文生 WU Yutao;JIA Wensheng(School of Mathematics and Statistics,Guizhou University,Guiyang 550025;Guizhou Provincal Key Laboratory of Game,Decision and Control System,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州省博弈决策与控制系统重点实验室,贵阳550025

出　　处：《系统科学与数学》2025年第1期172-180,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12061020,71961003);贵州省自然科学基金(20205016,2021088,20215640)资助课题。

摘　　要：良定性是最优化问题研究的热点之一,文章针对集值优化问题,考虑有限理性下该问题弱极小解集的广义Levitin-Polyak良定性和Levitin-Polyak良定性,并通过有限理性模型得到了其良定性的充分条件.更进一步,通过非线性分析和非紧测度的工具给出了集值优化问题Levitin-Polyak良定性的特征刻画.这些结果是新的且推广和改进了已有的一些结果.The study of well-posedness is one of the hot spots in optimization prob-lems.This paper considers generalized Levitin-Polyak well-posedness and Levitin-Polyak well-posedness of their weak minimal solution set under bounded rationality focusing on set-valued optimization problems.Besides,we obtain some sufficient conditions for their well-posedness by employing a bounded rationality model.Fur-thermore,by using tools such as nonlinear analysis and measures of noncompactness,the characterization of Levitin-Polyak well-posedness for the problem is given.These results are new and we generalize and improve some existing results.

关 键 词：集值优化问题 有限理性 Levitin-Polyak良定 弱极小解 

分 类 号：O224[理学—运筹学与控制论]