集值优化问题E-全局真有效解的非线性标量化定理  

Nonlinear scalar theorems of E-global proper solution for set-valued optimization problems

作　　者：仇秋生 潘铭敏 QIU Qiusheng;PAN Mingmin(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学与计算机科学学院

出　　处：《浙江师范大学学报（自然科学版）》2019年第4期379-385,共7页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11471291)

摘　　要：为了对线性空间中非凸集值优化问题的真有效解进行标量刻画,利用Gerstewitz泛函和改进集的性质,引入了实序线性空间中基于改进集的非凸分离定理,给出集值优化问题E-全局真有效解和E-弱有效解的非线性标量化定理,去掉了对目标函数和可行集的凸性要求.研究成果能够用于序锥代数内部为非空的集值优化问题.In order to give the scalar characterization of the proper efficient solution for the nonconvex set-valued optimization problems in linear space,the nonconvex separation theorems via improvement set in the real ordered linear space were introduced by the properties of Gerstewitz′s function and improvement set.The nonlinear scalar theorems of E -global proper efficient solutions and E -weakly efficient solutions for set-valued optimization problems were given without the convexity requirements for the objective functions and the feasible sets.The obtained results could be used to solve the set-valued optimization problems with nonempty algebraic interior of the ordered cone.

关 键 词：非线性标量化泛函 集值优化问题 改进集 非凸分离定理 E-全局真有效性 

分 类 号：O221.6[理学—运筹学与控制论]