应用数学和力学2025，Vol.46Issue(7)：926-938,13.DOI:10.21656/1000-0887.450273
两类集优化问题的Hadamard适定性研究
Hadamard Well-Posedness in 2 Types of Set Optimization Problems
摘要
Abstract
The Hadamard well-posedness of a set optimization problem(P)and an infinite set optimization problem(ISOP)under upper set order relation was studied.Firstly,in the case of the gamma convergence of the set-valued mapping sequence,the definitions of the generalized Hadamard well-posedness and the ε-gener-alized Hadamard well-posedness for(P)were given,the relationship between these 2 types of well-posedness-es were established,and the sufficient conditions for the Hadamard well-posedness of(P)were obtained.Then the sufficient conditions for the Hadamard well-posedness of(ISOP)were studied with the concept of Hausdor-ff cone-continuity under functional perturbations of both constraint sets and objective maps.The results im-prove those in the relevant previous references,enriching the study of set optimization problems.关键词
集优化问题/Hadamard适定性/Gamma-收敛/Hausdorff-锥连续Key words
set optimization problem/Hadamard well-posedness/Gamma-convergence/Hausdorff cone-conti-nuity分类
数理科学引用本文复制引用
程翔,彭再云,杨鑫,文铭..两类集优化问题的Hadamard适定性研究[J].应用数学和力学,2025,46(7):926-938,13.基金项目
国家自然科学基金(面上项目)(12271067) （面上项目）
重庆市自然科学基金面上项目(CSTB2024NSCQ-MSX0973) （CSTB2024NSCQ-MSX0973）
重庆市教委科技研究项目重点项目(KJZD-202200704) （KJZD-202200704）
重庆市高等教育教学改革研究项目重点项目(232072) （232072）
重庆市研究生教育教学改革项目(yjg223094) （yjg223094）
教育部协同育人项目(220503414180513) 本文作者衷心感谢重庆交通大学研究生科研创新项目(2024S0139)对本文的资助. （220503414180513）
