(h,)-Lipschitz函数及其广义方向导数和广义梯度  

The (h,)-Lipschitz Function, Its Generalized Directional Derivative and Generalized Gradient

作　　者：徐义红[1] 刘三阳[2] 

机构地区：[1]南昌大学数学系,南昌330047 [2]西安电子科技大学应用数学系,西安710071

出　　处：《数学物理学报（A辑）》2006年第2期212-222,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10461007);教育部全国优秀博士论文作者专项基金(200217)资助

摘　　要：借助于Ben—Tal广义代数运算引进了一种新的函数-(h,)-Lipschitz函数．讨论了它与Lipschitz函数之间的关系,给出了它的广义方向导数和广义梯度,得到了它们的若干性质．作为应用,给出了广义方向导数与切锥之间的关系。With the help of Ben-Tal＇s generalized algebraic operations, a new kind of functions, termed （h,φ）-Lipschitz functions, is introduced. The relationship between it and Lipschitz function is discussed. Generalized directional derivative and generalized gradient are developed and their properties are obtained. As an application, the relationship between generalized directional derivative and contingent cone is presented.

关 键 词：(h φ)-Lipschitz函数 广义方向导数 广义梯度 

分 类 号：O224[理学—运筹学与控制论]