集合优化问题解集的稳定性和扩展适定性  

Stability and extended well-posedness of the solution sets for set optimization problems

作　　者：孟旭东[1] MENG Xu-dong(Science and Technology College of Nanchang Hangkong University,Gongqingcheng 332020,Jiangxi,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《山东大学学报（理学版）》2022年第2期98-110,共13页Journal of Shandong University(Natural Science)

基　　金：江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(GJJ161597,GJJ218701)。

摘　　要：研究了集合优化问题近似解集的稳定性和扩展适定性。当目标函数具连续性和广义锥-拟凸性时,讨论了集合优化问题近似解集的Painlevé-Kuratowski上收敛和下收敛。结合适当假设条件,分析了集合优化问题的扩展适定性和弱扩展适定性。The stability and extended well-posedness of the approximate solution sets for set optimization problems are studied. The Painlevé-Kuratowski upper convergence and lower convergence of the approximate solution sets for set optimization problems are discussed by assuming the continuity and generalized cone quasi-convexity of objective function. The extended well-posedness and weak extended well-posedness for set optimization problems are analyzed under some appropriate assumptions.

关 键 词：集合优化问题 Painlevé-Kuratowski收敛 稳定性 扩展适定性 

分 类 号：O221.3[理学—运筹学与控制论]