强预不变凸函数的充要条件(英文)  

The Sufficiency and Necessity Conditions of Strongly Preinvex Functions

作　　者：唐万梅[1] 杨新民[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《运筹学学报》2006年第3期50-58,共9页Operations Research Transactions

基　　金：This research was partially supported by the National Natural Science Foundation of China(Grant No.10171118,10471159);the key project of the Chinese Ministry of Education,Supported by Program for New Century Excellent Talents in University.

摘　　要：本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件：(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性；(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性；(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性．In this paper, the relationships among strongly preinvex functions and preinvex functions, and strictly preinvex functions and semistrictly preinvex functions are discussed. Three sufficiency and necessity conditions are obtained： （i） Under certain condition, f is a strongly preinvex function if and only if f is a preinvex function and f satisfies intermediate-point strong preinvexity; （ii） Under certain condition, f is a strongly preinvex function if and only if f is a strictly preinvex function and f satisfies intermediatepoint strong preinvexity; （iii） Under certain condition, f is a strongly preinvex function if and only if f is a semistrictly preinvex function and f satisfies intermediate-point strong preinvexity.

关 键 词：运筹学 数学规划 强预不变凸函数 预不变凸函数 严格预不变凸函数 半严格预不变凸函数 

分 类 号：O177.91[理学—数学]