| R~n上的r-次微分与r-凸性 |
| |
| 引用本文： | 刘国志.R~n上的r-次微分与r-凸性[J].辽宁石油化工大学学报,1997(2). |
| |
| 作者姓名： | 刘国志 |
| |
| 作者单位： | 抚顺石油学院基础课教学部 |
| |
| 摘 要： | 提出了Ｒｎ上的ｒ－次微分与ｒ－凸性的概念，利用ｒ－次微分，给出了许多局部极小（极大）不能满足的全局极小（极大）的一个新的必要条件，利用ｒ－凸性给出了全局极小的充分条件。ｒ－凸函数是较凸函数更大的一类凸函数，有些ｒ－凸出数是处处不连续的，且ｒ－凸函数保持凸函数一些优良特性，ｒ－凸函数的局部极小总是全局极小。
|
| 关 键 词： | 次微分 凸 最优化 |
r-Subdifferential and r-Convexity of Functions On the R n |
| |
| Liu Guozhi.r-Subdifferential and r-Convexity of Functions On the R n[J].Journal of Liaoning University of Petroleum & Chemical Technology,1997(2). |
| |
| Authors: | Liu Guozhi |
| |
| Abstract: | The r-subdifferential and r-convexity of real-valued functions on the R n are introduced.By means of r-subdifferential,a new necessary condition for global minima is formulated which many local minima cann't satisfy.The r-convexity is used to state sufficient conditions for global minima.The r-convex functions are relatively large which are not continuous anywhere.Nevertheless,a local minimum of a r-convex function is always a global minimum. |
| |
| Keywords: | Subdifferential Convex Optimization |
| 本文献已被 CNKI 等数据库收录！ |
