集值优化问题的E-强有效解  

E-Strong Efficiency of Set-Valued Optimization Problems

作　　者：周志昂 刘爽 ZHOU ZHIANG;LIU SHUANG(College of Sciences,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《应用数学学报》2020年第5期882-896,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11971084,11861002);重庆市教委科学技术研究项目(KJZD-K202001104)资助。

摘　　要：本文主要研究了集值优化问题的E-强有效解.首先,基于改进集的概念,在实局部凸空间中引进了集合的E-强有效点,讨论了它与其它真有效点的关系.其次,在集值映射为邻近E-次似凸的条件下,建立了集值优化问题E-强有效解的标量化定理和Lagrange乘子定理.最后,获得了集值优化问题的E-强鞍点定理.这篇文章的结果统一和推广了一些文献中的已知结果.In this paper,E-strongly efficient solution of set-valued optimization problems is studied.Firstly,based on the concept of the improvement set,E-strongly efficient point of a set is introduced,and the relation between E-strongly efficient point and properly efficient point is discussed.Secondly,under the assumption of near E-subconvexlikeness of setvalued maps,scalarization theorems and Lagrange multiplier theorems of E-strongly efficient solution of set-valued optimization problems are established.Finally,E-strongly saddle point theorems of set-valued optimization problems are obtained.The results obtained in this paper unify and generalize some known results in the literature.

关 键 词：集值映射 改进集 邻近E-次似凸 E-强有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]