强CHIP性质和广义限制域逼近的特征  

Strong-CHIP and Characterization of the Best Approximation with Generalized Restrictions

作　　者：方东辉[1] 李冲[2] 杨文善[3] 

机构地区：[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

出　　处：《数学学报（中文版）》2004年第6期1115-1122,共8页Acta Mathematica Sinica：Chinese Series

基　　金：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.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.

关 键 词：强CHIP 最佳逼近 次强内点条件 广义限制域 

分 类 号：O174.41[理学—数学]