非光滑半无限多目标规划近似解的对偶和鞍点定理  

Duality and Saddle Point Theorems Of Approximate Solutions for Nonsmooth Semi-infinite Multiobjective Optimization Problems

作　　者：张雯 龙宪军[1] 黄应全[1] 李耿华 ZHANG WEN;LONG XIANJUN;HUANG YINGQUAN;LI GENGHUA(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《应用数学学报》2023年第4期532-548,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11471059,12001070);重庆市自然科学基金(cstc2018jcyjAX0119);重庆市研究生创新型科研项目(CYS21405);重庆市研究生导师团队项目(yds223010)资助。

摘　　要：本文利用切向次微分研究了一类非光滑半无限多目标规划问题,并讨论了它的对偶定理和鞍点定理.首先,建立了半无限多目标规划问题的Mond-Weir型对偶,在广义凸性假设下,获得了半无限多目标规划问题近似解的弱对偶、强对偶和逆对偶定理.其次,定义了向量值拉格朗日函数的ε-拟鞍点,获得了ε-拟鞍点的必要和充分条件.这些结论推广和改进了文献中的相应结果.最后以具体的例子来说明了本文的结论.In this paper,a class of nonsmooth semi-infinite multiobjective program-ming problems is considered by using tangential subdifferentials,and its dual and saddle theorems are discussed.Firstly,Mond-Weir type dual of semi-infinite multiobjective programming problems is established,under the assumptions of the generalized con-vexity,the weak duality,strong duality and inverse duality theorems of approximate solutions for semi-infinite multiobjective optimization problems are given.Secondly,the e-quasi-saddle of vector Langrange function is defined,then some necessary and sufficient conditions of the e-quasi-saddle point are derived.Our results extend and improve some known results,some examples are given to illustrate the main results of this paper.

关 键 词：半无限多目标规划 切向次微分 近似解 对偶 ε-拟鞍点 

分 类 号：O224[理学—运筹学与控制论]