非光滑广义Dini-凸多目标规划解的充分性与对偶性  

On Sufficiency and Duality of Solutions for Nonsmooth Generalized Dini-convex Multiobject Programming

作　　者：康瑞瑞[1] 张庆祥[2] 姜艳[2] 张文静[2] 

机构地区：[1]北京交通大学理学院,北京100044 [2]延安大学数学与计算科学学院,陕西延安716000

出　　处：《郑州大学学报（理学版）》2012年第2期13-19,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号61071144;陕西省教育厅专项科研基金资助项目;编号06JK152

摘　　要：利用Ben-Tal广义代数运算,给出了一种新的广义Dini右上方向导数和广义Dini梯度,引进了几类非光滑非凸函数的概念,在较弱的假设下,给出了广义Dini不变凸函数的一个充要条件,得到了非光滑广义Dini-凸多目标规划的最优性充分条件和几个对偶性结果.The generalized upper right directional Dini-derivative and Dini-gradient were given by using Ben-Tal＇ s generalized algebraic operations. Several classes of nonsmooth nonconvex functions （ general- ized Dini-convex） were introduced. Based on weaker assumptions, a sufficient and necessary condition for generalized Dini-invex functions was given, some optimal sufficient conditions and duality were ob- tained for a class of nonsmooth generalized Dini-convex multiobject programming.

关 键 词：非光滑 Dini-凸函数 多目标规划 充分性 对偶性 

分 类 号：O221.6[理学—运筹学与控制论]