强G-预不变凸函数的性质及应用  

Characteristics and Applications of Strongly G-preinvex Functions

作　　者：彭再云[1] 周选林[1] 赵勇[2] 

机构地区：[1]重庆交通大学理学院,重庆400074 [2]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2012年第4期12-17,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家青年基金(No.11001287);重庆市科委研究项目(No.CSTC2011AC6104;No.2010BB9254);重庆市教委资助课题(No.KJ120401)

摘　　要：在已有文献基础上继续讨论强G-预不变凸函数。首先用另外的例子来说明强G-预不变凸函数的存在性;然后给出了在上、下半连续性条件下f是强G-预不变凸函数的两个充要条件,借助于函数f的上图E(f),讨论了强G-预不变凸函数的一个刻画及强G-预不变凸函数簇的上确界性质;最后还获得了强G-预不变凸函数分别在两类数学规划问题中的应用,推广了已有文献的结果。In this paper, strongly G-preinvex function is further studied. Firstly, another example has been given to show its existence. Then, we give two necessary and sufficient conditions of strongly G-preinvex function under the condition of semicontinuity. By using the epigraph E＇ （f）, we also give a characterization and a property of strongly G-preinvex function respec- tively. Finally, by using strong G-preinvexity, important applications for two classes of mathematical programming problems are given. Our results extend and improve the exist ones in the literature.

关 键 词：不变凸集 G-预不变凸函数 强G预不变凸函数 数学规划 

分 类 号：O221.1[理学—运筹学与控制论]