关于预不变凸性准则的一个注记  

A note on criteria for preinvexity

作　　者：李素兰[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310032

出　　处：《浙江工业大学学报》2008年第1期116-118,共3页Journal of Zhejiang University of Technology

摘　　要：凸性和广义凸性在工程、管理科学、最优化理论及经济学中起着重要的作用.对凸性和广义凸性判别准则的研究是数学规划中最重要方面之一.杨于2001年在半连续性下给出了预不变凸性的准则.利用集合的稠密性和弱近似凸性,进一步刻画函数的预不变凸性.在较弱的条件下,得到了预不变凸性的一个等价命题.所使用的方法与杨用的方法不同.Convexity and generalized convexity play a key role in the engineering, management science, optimization theories and economics. The research on criteria for convexity and general- ized convexity is one of the most important aspects in mathematical programming. Yang presented criteria for preinvexity under semicontinuty in 2001. We research on describing preinvexity of functions in this paper by means of the density and weakly near convexity in the set. Under weaker conditions, we derive an equivalent proposition for preinvexity. The method described in this paper is different from Yang＇s.

关 键 词：预不变凸性 弱近似凸性 稠密性 

分 类 号：O212.2[理学—概率论与数理统计]