强预拟不变凸函数的充要条件(英文)  

The Sufficiency and Necessity Conditions of Strongly Prequasi-Invex Functions

作　　者：唐万梅[1] 刘茜[2] 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 [2]山东师范大学数学科学学院,济南250014

出　　处：《运筹学学报》2007年第3期21-30,共10页Operations Research Transactions

基　　金：This work is supported by the Natural Science Foundation of China (Grant No.10471159,No.10171118);NCET,Education Commission project Research Foundation of Chongqing(Grant No.KJ060818,KJ060804)

摘　　要：本文引入了一类新的广义凸函数—强预拟不变凸函数.讨论了强预拟不变凸函数与预拟不变凸函数、严格预拟不变凸函数及半严格预拟不变凸函数之间的关系,得到它的三个充要条件:(i)当条件P_1满足时,f是强预拟不变凸函数的充分必要条件是f是预拟不变凸函数且f满足中间点强预拟不变凸性;(ii)当条件P_2满足时,f是强预拟不变凸函数的充分必要条件是f是严格预拟不变凸函数且f满足中间点强顶拟不变凸性;(iii)当条件P_2满足时,f是强预拟不变凸函数的充分必要条件是f是半严格预拟不变凸函数且f满足中间点强预拟不变凸性.In this paper, a new type of generalized convex functions-strongly prequasi-invex functions is introduced. And the relationships among strongly prequasiinvex functions and prequasi-invex functions, and strictly prequasi-invex functions and semistrictly prequasi-invex functions are discussed. Three sufficiency and necessity conditions of strongly prequasi-invex functions are obtained： （i） Under Condition P1, f is a strongly prequasi-invex function if and only if f is a prequasi-invex function and f satisfies intermediate-point strong prequasi-invexity; （ii） Under Condition P2, f is a strongly prequasi-invex function if and only if f is a strictly prequasi-invex function and f satisfies intermediate-point strong prequasi-invexity; （iii） Under Condition P2, f is a strongly prequasi-invex function if and only if f is a semistrictly prequasi-invex function and f satisfies intermediate-point strong prequasi-invexity.

关 键 词：数学规划 强预拟不变凸函数 预拟不变凸函数 严格预拟不变凸 函数 半严格预拟不变凸函数 

分 类 号：O221.2[理学—运筹学与控制论]