基于拟相对内部集值优化问题弱有效元的最优性条件  

The Optimality Conditions of Weakly Efficient Element for Set-valued Optimization Problems Based on Quasi-relative Interior

作　　者：吴唯钿 仇秋生[1] WU WEITIAN;QIU QIUSHENG(Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;College of Mathematics,Sichuan University,Chengdu 610065,China)

机构地区：[1]浙江师范大学数学系,金华321004 [2]四川大学数学学院,成都610065

出　　处：《应用数学学报》2021年第1期145-158,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金资助项目(11471291)。

摘　　要：本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.In this paper,we study the optimality conditions of weakly efficient element for nonconvex set-valued optimization problems based on quasi-relative interior.Firstly,the relationship between weakly efficient element and linear subspace is discussed,by using separation theorem involving the quasi-relative interior,optimality conditions of weakly efficient element is obtained.Then,Lagrange multiplier theorem of weakly efficient element based on quasi-relative interior is presented.

关 键 词：集值优化 弱有效元 拟相对内部 最优性条件 LAGRANGE乘子定理 

分 类 号：O221.6[理学—运筹学与控制论]