含参向量优化问题的Lipschitz连续性  

Lipschitz continuity for parametric vector optimization problems

作　　者：孟旭东[1] MENG Xudong(Science and Technology College of Nanchang Hangkong University, Gongqingcheng 332020, China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《大连理工大学学报》2021年第2期212-220,共9页Journal of Dalian University of Technology

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：在赋范空间中研究了含参向量优化问题的Lipschitz连续性.在目标函数和可行集分别受参数扰动的情况下,给出了含参向量优化问题的弱解映射、解映射、弱最优值映射及最优值映射的上Lipschitz连续性和下Lipschitz连续性的充分条件.研究结果表明,含参向量优化问题的(弱)解映射的上(下)Lipschitz连续性和(弱)最优值映射的上(下)Lipschitz连续性皆具有统一性规律.Lipschitz continuity for parametric vector optimization problems in normed spaces is studied.Some sufficient conditions for the upper Lipschitz continuity and the lower Lipschitz continuity of the weak solution mapping,the solution mapping,the weak optimal value mapping and the optimal value mapping are given under the case that the objective function and the feasible set are perturbed by parameters respectively.The results show that the upper(lower)Lipschitz continuity of(weak)solution mappings and the upper(lower)Lipschitz continuity of(weak)optimal value mappings for parametric vector optimization problems are uniform.

关 键 词：向量优化问题 解映射 最优值映射 LIPSCHITZ连续性 

分 类 号：O221.3[理学—运筹学与控制论]