非光滑多目标半无限规划问题的混合型对偶  

Mixed Type Duality for Nonsmooth Multiobjective Semi⁃Infinite Programming Problems

作　　者：刘娟 龙宪军[1] LIU Juan;LONG Xianjun(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,P.R.China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《应用数学和力学》2021年第6期595-601,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(11471059);重庆市基础与前沿研究计划项目(cstc2018jcyjAX0119;cstc2020jcyj⁃msxmX0053);重庆市教育委员会科学技术研究重点项目(KJZD⁃K201900801);重庆市巴渝学者特聘教授专项资助。

摘　　要：该文研究了非光滑多目标半无限规划问题的混合型对偶.首先,利用Lagrange函数介绍了非光滑多目标半无限规划混合型对偶的弱有效解和有效解的定义.其次,利用Dini⁃伪凸性建立了非光滑多目标半无限规划混合型对偶的弱对偶定理、强对偶定理和逆对偶定理.该文所得结果推广了已有文献中的主要结果.The mixed type duality for nonsmooth multiobjective semi⁃infinite programming problems was stud⁃ied.Firstly,by the Lagrange function,the definitions of weakly efficient solutions and efficient solutions to the mixed type duality were introduced.Secondly,by means of the Dini⁃pseudoconvexity,the weak duality theo⁃rems,the strong duality theorems and the converse duality theorems were obtained.The results generalize the main results in previous literatures.

关 键 词：多目标半无限规划 Dini⁃伪凸 混合型对偶 

分 类 号：O221.2[理学—运筹学与控制论]