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| 强CHIP性质和广义限制域逼近的特征 | |
| 引用本文： | 方东辉,李冲,杨文善.强CHIP性质和广义限制域逼近的特征[J].数学学报,2004,47(6):1115-112. |
| 作者姓名： | 方东辉 李冲 杨文善 |
| 作者单位： | 1. 吉首大学数学与计算机科学系,吉首,416000 2. 浙江大学数学系,杭州,310028 3. 浙江师范大学数理信息学院,金华,321004 |
| 基金项目： | 国家自然科学基金资助项目(10271025)，浙江省自然科学基金资助项目(102058) |
| 摘 要： | 本文研究了广义限制域的最佳逼近问题,在允许有有限个节点的情况下,引入次强内点条件的概念,并将优化理论中的强CHIP性质等概念应用到本文所研究的问题中,刻画了次强内点、强CHIP性质和最佳逼近的特征之间的关系.作为推论,我们得到了广义限制最佳逼近的Kolmogorov型和“零属于凸包”型等特征定理. |
| 关 键 词： | 最佳逼近 强CHIP 次强内点条件 |
| 文章编号： | 0583-1431(2004)06-1115-08 |
Strong-CHIP and Characterization of the Best Approximation with Generalized Restrictions |
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| Dong Hui FANG.Strong-CHIP and Characterization of the Best Approximation with Generalized Restrictions[J].Acta Mathematica Sinica,2004,47(6):1115-112. | |
| Authors: | Dong Hui FANG |
| Institution: | Dong Hui FANG (Department of Mathematics and Computer Science, Jishou University, Jishou 416000, P. R. China) Chong LI (Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China) Wen Shan YANG (College of Mathematics, Physics and Information Science, Zhejiang Normal University, Jinhua 321004, P. R. China) |
| Abstract: | The problem of the best approximation with generalized restrictions is in-vestigated. Under the assumption that l and u have finite intersection points, by introducing the concept of the sub-strong interior point condition and making use of the strong-CHIP from optimization theory, we study the relationship of the sub-strong interior point, the strong-CHIP and the characterization of the best approximation with generalized restrictions. Consequently, the characterization theorems of Kolmogorov's type and "0 belonging to the convex hull" type are obtained. |
| Keywords: | The best approximation Strong-CHIP Sub-strong interior point condition |
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