向量优化问题的最优性条件与全对偶之研究  

Optimality Conditions and Total Dualities for Vector Optimization Problems

作　　者：郑晴慧 王仙云[1] 方东辉[1] ZHENG Qinghui;WANG Xianyun;FANG Donghui(College of Mathematics and Statistics,Jishou University,Jishou 416000)

机构地区：[1]吉首大学数学与统计学院,吉首416000

出　　处：《系统科学与数学》2024年第6期1709-1722,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(12261037,11861033);湖南省自然科学基金(2024JJ7396);湖南省教育厅科研基金(CX20221112)资助课题。

摘　　要：利用向量函数的次微分性质,引入新的弱性约束规范条件,等价刻画了向量优化问题的KKT类最优性条件.然后,利用共轭映射的性质,定义了该问题的Largrange、FenchelLargrange和Toland-Fenchel-Lagrange对偶问题,建立了向量优化问题与三类对偶问题之间的全对偶和稳定全对偶定理,推广和改进了前人的相关结论.In this paper,by using the properties of subdifferential of vector functions,we introduce some new weaker constraint qualifications.By using those constraint qualifications,optimality conditions for the vector optimization problem are established.Moreover,by using the properties of conjugate map,we define the Lagrange,Fenchel-Lagrange and Total-Fenchel-Lagrange type dual problems for the vector optimization problem.Under these constraint qualifications,the total duality and the stable total duality between vector optimization problem and its three types of dual problems are established.Our results extend the corresponding results in the previous papers.

关 键 词：向量优化问题 约束规范条件 最优性条件 全对偶 

分 类 号：O224[理学—运筹学与控制论]