锥拟凸集值映射多目标优化的解集的连通性(英文)  

Connectedness of the Solution Set of Multiobjective Optimization with Cone Quasiconvex Set-Valued Mapping

作　　者：凌晨[1] 

机构地区：[1]浙江财经学院统计运筹系,杭州310012

出　　处：《运筹学学报》2001年第2期33-40,共8页Operations Research Transactions

摘　　要：在一般拓扑向量空间中，本文引进了一类锥拟凸（锥严格拟凸）集值映射．并在目标映射是锥拟凸（锥严格拟凸）和上半连续的条件下，利用 Minkowski泛函，证明了弱有效解（有效解）集是连通的．文[9]中的结论是本文所得结果在目标映射为单值和拓扑空间为格的情况下的特例．In this paper, we introduce a class of cone quasiconvex (cone strictly quasiconvex) set- valued mapping in general topological vector spaces. Under the condition that objective mapping is cone quasiconvex (cone strictly quasiconvex) and upper semicontinuous, we prove that the weak efficient solution (efficient solution) set is connected, by using a Minkowski function. The results obtained by Fu in [9] could be deemed as special example of our conclusion in that its objective mapping is single value and the topological vector spaces is lattice.

关 键 词：集值映射 多目标优化 锥拟凸 有效解 连通性 拓扑向量空间 MINKOWSKI泛函 

分 类 号：O224[理学—运筹学与控制论]