Some Minimax Problems in Lexicographic Order

作     者：Yu ZHANG Sheng-jie LI 

作者机构：College of Statistics and MathematicsYunnan University of Finance and Economics College of Mathematics and StatisticsChongqing University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2017年第33卷第1期

页      面：193-200页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11171362 11571055) 

主　　题：vector Optimization Minimax theorem Lexicographic saddle point lexicographic equilibriumproblem 

摘      要：In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.