变序结构集优化问题的适定性  

Well-posedness for Set Optimization with a Variable Ordering Structure

作　　者：刘越庆 徐义红[1] LIU Yueqing;XU Yihong(Department of Mathematics,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《应用数学》2025年第1期182-190,共9页Mathematica Applicata

基　　金：国家自然科学基金项目(11961047);江西省研究生创新专项资金项目(YC2023-S021)。

摘　　要：本文研究具有变序结构集优化问题的适定性.基于广义变下序关系(variable generalized lower less relation),给出了集优化问题的三种适定性概念.引进了近似解映射,讨论了该映射的性质.给出了具有变序结构集优化问题的三种适定性的充分条件.举例说明了文中的主要结果.This paper investigates the well-posedness for set optimization with a variable ordering structure.Based on the variable generalized lower less relationship,three concepts of well-posedness are introduced for set optimization.An approximate solution mapping is introduced,and its properties are discussed.Three kinds of optimality sufficient conditions of the well posedness are established for set optimization with a variable ordering structure.Some examples are given to illustrate the main results.

关 键 词：适定性 集优化 共辐射集 变序结构 

分 类 号：O221.6[理学—运筹学与控制论]