| (h,φ )-Lipschitz函数及其广义方向导数和广义梯度 |
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| 引用本文： | 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(A辑),2006,26(2):212-222. |
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| 作者姓名： | 徐义红 刘三阳 |
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| 作者单位： | [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 |
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| 基金项目： | 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 |
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| 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.
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| 关 键 词： | (h φ)-Lipschitz函数 广义方向导数 广义梯度 |
| 文章编号： | 1003-3998（2006）02-212-11 |
| 收稿时间： | 2003-09-20 |
| 修稿时间： | 2004-12-20 |
(h,φ)-Lipschitz Function, Its Generalized Directional Derivative and Generalized Gradient |
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| Xu Yihong,Liu Sanyang.(h,φ)-Lipschitz Function, Its Generalized Directional Derivative and Generalized Gradient[J].Acta Mathematica Scientia,2006,26(2):212-222. |
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| Authors: | Xu Yihong Liu Sanyang |
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| Institution: | Department of Mathematics, Nanchang University, Nanchang |
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| 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. |
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| Keywords: | (h φ)-Lipschitz functionzz Generalized directional derivativezz Generalized gradient
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