向量优化中改进集的一个性质  

A Characterization of Improvement Set in Vector Optimization

作　　者：林安[1] 刘学文[1] 

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2016年第2期1-3,共3页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11301574)

摘　　要：改进集是研究向量优化问题十分重要的工具之一。基于改进集对偶锥和回收锥的一些基本性质在适当假设条件下证明了对于有限维空间R^n中两个闭集E_1,E_2,若cl(cone(conv E_1))是点的,则E_1,E_2之和E-1+E_2仍为闭集。并提出了一些具体例子对主要结果进行了解释,指出若cl(cone(conv E_1))不是点的,其结论不一定成立。Improvement set is one of the most important tools to study vector optimization problems. In this paper, by some basic dual characterizations of improvement sets and some tools including as recession cone, the closedness of a sum of two closed sets E1 and E2 is proved if cl（cone（conv E1 ）） is pointed under some suitable assumption conditions in finite dimensional space R＂. Moreo- ver, some concrete examples also are presented to illustrate the main results and show that the closedness of a sum of two closed sets may be invalid if cl（cone（conv El ）） is not pointed.

关 键 词：改进集 对偶性质 回收锥 向量优化 

分 类 号：O221.6[理学—运筹学与控制论]