(h,φ )-Lipschitz函数及其广义方向导数和广义梯度

数学物理学报

(h,φ )-Lipschitz函数及其广义方向导数和广义梯度

徐义红;刘三阳

南昌大学数学系南昌 330047

收稿日期:2003-09-20 修回日期:2004-12-20 出版日期:2006-04-25 发布日期:2006-04-25
通讯作者: 徐义红
基金资助:
国家自然科学基金(10461007)和教育部全国优秀博士论文作者专项基金(200217)资助

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

Xu Yihong;Liu Sanyang

Department of Mathematics, Nanchang University, Nanchang

Received:2003-09-20 Revised:2004-12-20 Online:2006-04-25 Published:2006-04-25
Contact: Xu Yihong

摘要/Abstract

摘要： 借助于Ben-Tal广义代数运算引进了一种新的函数--- (h,φ)-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.

关键词: (h,φ)-Lipschitz函数, 广义方向导数, 广义梯度

Abstract:

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.

Key words: (h,φ)-Lipschitz function, Generalized directional derivative, Generalized gradient

中图分类号:

90C29

徐义红;刘三阳.

(h,φ )-Lipschitz函数及其广义方向导数和广义梯度

[J]. 数学物理学报, 2006, 26(2): 212-222.

Xu Yihong;Liu Sanyang.

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

[J]. Acta mathematica scientia,Series A, 2006, 26(2): 212-222.

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