参数强向量原始与对偶均衡问题解映射的Lipschitz连续性  

Lipschitz continuity of solution mappings to parametric strong vector primal and dual equilibrium problems

作　　者：孟旭东[1] 周蓉 MENG Xudong;ZHOU Rong(Science College of Nanchang Hang kong University,Gongqingcheng,Jiangxi 332020,China;Shenzhen Guanlan No.2 Middle School,Shenzhen,Guangdong 51800,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020 [2]深圳市观澜第二中学,广东深圳51800

出　　处：《南昌大学学报（理科版）》2020年第4期313-316,322,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11201216);江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614);江西省教育厅科学技术研究项目(GJJ161597)。

摘　　要：在赋范线性空间中研究参数强向量原始与对偶均衡问题解映射的Lipschitz连续性。给出了参数强向量原始与对偶均衡问题有效解的概念,提出了向量函数的强凸(凹)性和单调性,应用分析方法建立了参数强向量原始与对偶均衡问题解映射Lipschitz连续的充分性定理。研究表明,参数强向量原始与对偶均衡问题解映射Lipschitz连续的结论具有统一性。The Lipschitz continuity of solution mappings to parametric strong vector primal and dual equilibrium problems is studied in normed linear spaces.The concepts of efficient solution for these corresponding equilibrium problems are given,and the strong convexity(concavity)and monotonicity for vector functions are proposed.Theorems are established by using analytical method to give sufficient conditions for the Lipschitz continuity of solution mappings to parametric strong vector primal and dual equilibrium problems..The research shows that the conclusion for Lipschitz continuity of solution mappings to parametric strong vector primal and dual equilibrium problems is unified.

关 键 词：LIPSCHITZ连续性 参数强向量均衡问题 对偶问题 有效解 

分 类 号：O221.3[理学—运筹学与控制论]