Banach空间中显凸泛函的两个充分条件  

Two Sufficient Conditions of Explicit Convex Functions in Banach Spaces

作　　者：刘彩平[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：《重庆师范大学学报（自然科学版）》2006年第4期18-20,共3页Journal of Chongqing Normal University:Natural Science

摘　　要：在Banach空间中给出了显凸泛函的概念,然后利用泛函的G-可微性,给出了显凸泛函的两个充分条件。即如果泛函J∶V→R在V中是G-可微的,且其G-微分满足1)u,v∈V,J(u)≠J(v),有J′(v,u-v)<J(u)-J(V);或者2),u,v∈V,J(u)≠J(v),有J′(u,u-v)-J′(v,u-v)>0,那么J在V中是显凸的。In this paper,the concept of explicit convex function is given,then tow sufficient conditions of explicit convex functions are obtained by using G-differentiability of functions in Banach space.They are that if J∶V→R is G-differentiable in V,either 1)and if for any u,v∈V with J(u)≠J(v),we have J~′(v,u-v)<J(u)-J(v);or 2),if for any u,v∈V with J(u)≠J(v),we have J~′(u,u-v)-J~′(v,u-v)>0,then J is explicit convex function in V.

关 键 词：显凸泛函 G-微分 充分条件 

分 类 号：O221[理学—运筹学与控制论]