集优化问题的近似Benson真有效解及非线性刻画  

Approximate Benson Properly Efficient Solutions and Nonlinear Characterizations of Set Optimization Problems

作　　者：杨兴宇 黄斌 徐义红[1] YANG Xingyu;HUANG Bin;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》2022年第2期412-418,共7页Mathematica Applicata

基　　金：国家自然科学基金(11961047);江西省自然科学基金基金(20192BAB 201010);南昌大学科研训练项目(55002052)。

摘　　要：利用集合的Minkowski差,引进集优化问题的Benson真有效解和近似Benson真有效解的概念,讨论了它们之间的关系.在某种假设下证明了近似Benson真有效解集是闭的.利用非线性泛函分别建立了无约束和带约束集优化问题取得近似Benson真有效解的必要条件.By using the Minkowski difference of sets,the concepts of Benson properly efficient solutions and approximate Benson properly efficient solutions are introduced for set optimization problems,and the relationship between them is discussed.It is proved that the set of approximate Benson properly efficient solution is closed under some assumptions.By using nonlinear functionals,the necessary conditions are established for unconstrained and constrained set optimization problems obtain approximate Benson properly efficient solutions,respectively.

关 键 词：集优化 Minkowski差 BENSON真有效解 非线性泛函 

分 类 号：O221[理学—运筹学与控制论]