非凸集值优化问题弱Benson真有效解的高阶最优性条件  

Higher order optimality conditions for weakly Benson proper efficient solutions of nonconvex set-valued optimization problems

作　　者：王开荣[1] 王义利[1] 曹伟[1] 

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《华东师范大学学报（自然科学版）》2011年第3期59-67,99,共10页Journal of East China Normal University(Natural Science)

基　　金：重庆市科委资助项目(2008BB0346)

摘　　要：首先,给出了一些必要的基本概念和重要引理.其次,讨论了高阶广义切集的一些重要性质.最后,利用这些性质和Gerstewitz非凸分离泛函,在目标映射以及约束映射没有任何凸性假设的条件下,获得了带广义不等式约束的集值优化问题弱Benson真有效解的高阶必要和充分最优性条件.同时,给出例子说明了所获得的结果推广了文献中的相应结果.Firstly,some necessarily basic concepts and an important lemma were given.Secondly,some important properties of generalized higher-order tangent sets were discussed.Finally,by virtue of those properties and the Gerstewitz＇s nonconvex separation functional,necessary and sufficient optimality conditions were obtained for weakly Benson proper efficient solutions of set-valued optimization problems without any convexity assumption on objective and constraint mappings.Moreover,two examples were given to show that the result obtained is a generalization to the corresponding results in literatures.

关 键 词：集值优化 广义高阶相依集 非凸分离泛函 BENSON真有效解 高阶最优性条件 

分 类 号：O224[理学—运筹学与控制论]