基于改进集的集值Ekeland变分原理  

Ekeland′s variational principle via improvement sets for set-valued maps

作　　者：万轩 张万里[2] 赵克全[2] 

机构地区：[1]重庆电讯职业学院基础部,重庆402247 [2]重庆师范大学数学学院,重庆401331

出　　处：《纯粹数学与应用数学》2015年第6期567-574,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(11301574;11271391);重庆市基础与前沿研究计划项目(cstc2015jcyj A00027);重庆市教委科学技术研究项目(KJ1500303);第二批重庆市高等学校青年骨干教师资助计划

摘　　要：Ekeland变分原理在最优化理论及应用研究中具有十分重要的作用.利用非线性标量化函数及相应的非凸分离定理建立了基于改进集的集值Ekeland变分原理.新的Ekeland变分原理包含了一些经典的Ekeland变分原理作为其特例.Ekeland′s variational principles have been playing a very important role in optimization theory and it′s applications. In this paper, based on improvement sets, we establish an Ekeland′s variational principle for set-valued maps by using a kind of nonlinear scalarization function and its corresponding nonconvex separation theorem. New Ekeland′s variational principle includes some classical Ekeland′s variational principles as its special cases.

关 键 词：改进集 EKELAND变分原理 集值映射 非线性标量化函数 

分 类 号：O176[理学—数学] O177.9[理学—基础数学]