集值优化问题Proximal真有效解集的连通性  

The connectedness of the Proximal proper efficient solutions sets for set-valued optimization

作　　者：李小燕[1] 岳瑞雪[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《周口师范学院学报》2015年第5期14-16,120,共4页Journal of Zhoukou Normal University

基　　金：国家自然科学基金(No.11201511)

摘　　要：研究集值优化问题Proximal真有效解集的连通性.首先在一种广义凸性假设下,证明了集合的Proximal真有效点集的连通性.其后,针对集值优化问题,在目标映射为锥凸和上半连续的条件下,证明了Proximal真有效解集的连通性.In this paper, we study the connectedness of the Proximal proper efficient solutions sets of the optimization problem for a set- valued mapping. Firstly, we prove that the Proximal proper efficient point set is connected under a kind of generalized convexity assumption, secondly, for set - valued optimization, we present that if the objective function is a cone - convex set - valued and upper semi - continuous mapping , then the Proximal efficient solution set is also connected.

关 键 词：Proximal真有效解 连通性 集值映射 上半连续 

分 类 号：O221.6[理学—运筹学与控制论]