| 广义拟可微函数的微分 |
| |
| 引用本文： | 张宏伟,张立卫,夏尊铨.广义拟可微函数的微分[J].运筹学学报,2007,11(2):17-30. |
| |
| 作者姓名： | 张宏伟 张立卫 夏尊铨 |
| |
| 作者单位： | 大连理工大学应用数学系,大连,116024 |
| |
| 摘 要： | 本文给出一种广义拟可微函数类,它是Demyanov与Rlubinov(1980)意义下拟可微函数的推广,通过凸集类对的空间的某些理论,建立了这类广义拟可微函数的微分学理论,包括加法运算、数乘运算、乘法运算、除法运算、极大值运算,极小值运算以及复合运算的微分公式和中值定理。这些结果为广义拟可微类函数优化研究提供了基本工具．
|
| 关 键 词： | 运筹学 非光滑优化 方向可微函数 方向导数 拟可微函数 拟微分 广义拟可微函数 广义拟微分 中值定理 |
| 修稿时间： | 2003-11-24 |
Differentials of Generalized Quasi-Differentiable Functions |
| |
| Zhang Hongwei,Zhang Liwei,Xia Zunquan.Differentials of Generalized Quasi-Differentiable Functions[J].OR Transactions,2007,11(2):17-30. |
| |
| Authors: | Zhang Hongwei Zhang Liwei Xia Zunquan |
| |
| Institution: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
| |
| Abstract: | A class of generalized quasi-differentiable functions,as an extension of the class of quasi-differentiable functions in the sense of Demyanov and Rubinov(1980),is studied systematically in this paper.Based on the theory of the space of pairs of convex-set collections proposed by17],the calculus theory of generalized quasi-differential is estab- lished,including the operations of scalar multiplication,multiplication,division,pointwise maximum,pointwise minimum and composition.And several mean-value theorems are demonstrated as well.The proposed calculus theory provides a foundation for the study on generalized quasi-differentiable optimization. |
| |
| Keywords: | Operations research nonsmooth optimization directional differentiable function directional derivative quasi-differentiable function quasi-differential generalized quasi-differentiable function generalized quasi-differential |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
