【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.更多还原

【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.更多还原