锥意义下有效解的本质集与本质连通区  

Essential Set and Essential Component of Efficient Solutions on the Cone

作　　者：陈源[1] 

机构地区：[1]衡阳师范学院数学系,湖南衡阳421008

出　　处：《河南师范大学学报（自然科学版）》2008年第2期17-19,共3页Journal of Henan Normal University(Natural Science Edition)

摘　　要：有效解不具有上半连续性,也不具有下半连续性,本质有效解也未必总是存在,鉴于此,主要研究了锥意义下向量优化问题有效解的本质集与本质连通区,采取构造函数的方法、反证法和usco的方法,得到了锥意义下有效解集的非空闭子集本质的一个充分必要条件,得出了与有效解的本质集和本质连通区有关的其他结果.The efficient solutions have no properties of the upper semi-continuity and the lower semi-continuity as well as the efficient solutions which are essential always do not exist, therefore the paper mainly researches the essential set and the essential component of efficient solutions on the cone for vector optimization question. In this paper, it uses a method of constructing function, reduction to absurdity and a way of usco. For the nonempty and closed subset of the efficient solutions＂ set, which is essential on the cone, this paper gives an efficient and necessary condition and some consequent results relating to the essential set and the essential component of efficient solutions.

关 键 词：锥 有效解 本质集 本质连通区 

分 类 号：O177.24[理学—数学]