基于变动控制结构的集优化问题的广义适定性  

Generalized well-posedness for set optimization problems based on variable ordering structures

作　　者：刘园园 王三华[1] 李秋英[2] 张鹏 LIU Yuanyuan;WANG Sanhua;LI Qiuying;Zhang Peng(Department of Mathematics,Nanchang University,Nanchang 330031,China;Nanchang University College of Science and Technology,Gong Qingcheng 332020,China;Institute for Advanced Study,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学数学系,江西南昌330031 [2]南昌大学科学技术学院,江西共青城332020 [3]南昌大学高等研究院,江西南昌330031

出　　处：《南昌大学学报（理科版）》2023年第1期1-9,共9页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11661055,71971102,12061045);江西省自然科学基金资助项目(20212BAB201028);江西省教育厅科学技术研究项目(GJJ2203906,GJJ2203905)。

摘　　要：讨论基于变动控制(偏序)结构的集优化问题的广义适定性。利用变动偏序结构,引进了关于集合的两种不同变动序关系,进而给出了集优化问题相应的广义适定性概念。提出了近似解集并讨论了其性质。运用这些性质,在目标映射具适当的半连续性条件下,获得了集优化问题关于变动序结构的广义适定性的充分性条件与必要性条件。给出了若干例子,用以说明所得主要结果的正确性。由于变动偏序结构是固定偏序结构的自然推广,所得主要结果推广和发展了本领域的近期相关研究成果。Based on variable ordering structures, generalized well-posedness is mainly discussed in this paper for set optimization problems.With the help of variable ordering structures, two different kinds of variable ordering relations are introduced for sets.The corresponding concepts of generalized well-posedness are proposed for set optimization problems.Approximation solution sets are defined and their properties are studied.Furthermore, by using these properties, sufficient and necessary conditions of generalized well-posedness are obtained for set optimization problems, which are based on variable ordering structures.Some examples are also given to illustrate the validity of the main results obtained in this paper.Since the variable ordering structure is a natural generalization of the fixed one, the main results obtained in this paper extend and develop some recent corresponding researches in this field.

关 键 词：集优化问题 广义适定性 变动控制结构 变动序关系 

分 类 号：O221.6[理学—运筹学与控制论]