含约束映射的强有效问题解集的连通性  

Connectedness of Efficient Solution Set for Strong efficiency Problem With Constraints

作　　者：曹敏[1] 陈剑尘[1] 高洁[1] 

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2014年第1期33-38,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11061023);国家自然科学基金(AA2012O7155);江西省自然科学基金(2010GZS0176);南昌航空大学博士启动基金(EA200907383);南昌航空大学研究生科技创新基金(YC2012021)

摘　　要：集值映射理论及集合拓扑理论在集值优化问题的稳定性研究中起着重要作用。文章在局部凸空间中利用这些理论研究了含约束映射集值优化问题强有效解集的连通性。首先给出了一个强有效解的基泛函标量化的结论,探讨了弧连通映射的一些性质,然后在可行域为弧连通的情况下给出了一个含约束映射有效点集连通性的引理,最后利用该引理研究了在可行域为弧连通的情况下含约束映射有效解集的连通性,得到一个含约束映射有效解集的连通性定理。由于凸集一定是弧连通的,反之则不然,故该研究拓宽了可行域的限制。Set-valued mappings theory and set topology theory play an important role in the stability study of set-valued optimization. In this paper, we use these theories to study the connectedness of strong efficient solution set for set-valued constrained optimization problems in locally convex spaces. Firstly, we give a conclusion of the scalarization of base functions, and discuss some properties of eone-arcwise connected set-valued mapping. Then, we give a lemma of the connectedness of strong efficient point set for set-valued constrained optimization problems when the feasible region is an arewise connected and compact subset. At last, using this lemma, we study the eonnectedness of strong efficient solution set with constraints and obtain a theorem of the connectedness of strong efficient solution set with constraints. The convex sets are arc-wise connected sets and the converse is not true in general, so this study broadens the restrictions of the feasible region in some degree.

关 键 词：集值映射 强有效解 弧连通 

分 类 号：O317[理学—一般力学与力学基础]