具变动控制结构的对称广义强向量拟均衡问题及其应用  

Symmetric Generalized Strong Vector Quasi-Equilibrium Problem with Variable Ordering Structures with Applications

作　　者：黄文君 王三华[1,2] 张宇新 HUANG Wenjun;WANG Sanhua;ZHANG Yuxin(Department of Mathematics,Nanchang University,Nanchang 330031;Post-Doctor Station of Management Science and Engineering,Nanchang University,Nanchang 330031)

机构地区：[1]南昌大学数学系,南昌330031 [2]南昌大学管理科学与工程博士后流动站,南昌330031

出　　处：《系统科学与数学》2020年第6期1037-1049,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11661055,11801257,11661056,11771198);江西省自然科学基金(20151BAB201020);中国博士后科学基金(2015M582047);江西省博士后科研择优资助项目(2016KY58);江西省教育厅科学基金(GJJ160063);江西省研究生创新专项资金(YC2019-S021)资助课题。

摘　　要：讨论了具变动控制结构的对称广义强向量拟均衡问题.在锥值映射具无限上连续性条件下,利用Fan-KKM定理和Kakutani-Fan-Glicksberg不动点定理,建立了解的存在性结果,进一步,还得出了其解集的紧性结论.作为应用,文中还给出了广义强向量拟鞍点问题解的存在性及其解集的紧性结果.这些结果推广和发展了近期已有文献的相关结论.In this paper,a symmetric generalized strong vector quasi-equilibrium problem with variable ordering structures is introduced and discussed.Under the condition of cosmically upper continuity for the cone-valued mapping,some existence theorems are obtained by using the Fan-KKM theorem and the Kakutani-FanGlicksberg fixed point theorem.Moreover,the conclusions of compactness of the solution set for this problem are also derived.As an application,some theorems of existence of solutions and compactness of solution set are obtained for generalized strong vector quasi-saddle point problem.These results extend and develop some corresponding ones existing in the recent literatures.

关 键 词：对称广义强向量拟均衡问题 鞍点问题 变动控制结构 解的存在性 无限上连续 

分 类 号：O224[理学—运筹学与控制论]