Banach空间上的光滑变分原理

Banach Space on the Smooth Variational Principle

光滑变分原理的意义不只在于优化理论方面,它在控制理论,不动点理论与大范围的分析领域有非常广泛的应用,Borwein-Preiss光滑变分原理也是其应用非常广泛的定理,但应用条件较苛刻,为解决此问题,把Borwein-Preiss光滑变分原理推广到希尔伯特空间以及巴拿赫空间中更一般的形式。

This paper mainly consider the smooth variational principle,variational principle singnificance lies not only in its optimization theory,control theory,fixed point theory and analysis of large scale is also very wide application, Borwein-Preiss smooth variational principle is used widely, but the application of relatively harsh conditions, in order to solve this problem, the Borwein-Preiss smooth become more general form principle is extended to Hilbert spaces and Banach spaces.