Optimality Conditions for Minimax Optimization Problems with an Infinite Number of Constraints and Related Applications  

作　　者：Li-nan ZHONG Yuan-feng JIN 

机构地区：[1]Department of Mathematics,College of Science,Yanbian University,Yanji 133002,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第2期251-263,共13页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11761072);the Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(No.20200301053RQ)。

摘　　要：This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for optimal solutions to the problem(MMOP)by means of employing some advanced tools of variational analysis and generalized differentiation.Then,sufficient conditions for the existence of such solutions to the problem(MMOP)are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions.Finally,some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints,and a necessary optimality condition for a quasiε-solution to problem(MMOP).

关 键 词：minimax programming problem semi-infinite optimization limiting subdifferential multiobjective optimization approximate solutions 

分 类 号：O224[理学—运筹学与控制论]