论文标题
Banach空间中功能的变分凸度
Variational Convexity of Functions in Banach Spaces
论文作者
论文摘要
本文介绍了Banach空间上扩展价值功能的变异凸度的研究和表征。该概念最近是由Rockafellar引入的，其重要性已经实现并应用于有限维空间中的连续优化问题。在这里首次研究的无限维空间中的变异凸度明显更多，需要使用强大的几何功能分析工具以及变异分析和Banach空间中的广义差异化。
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and applied to continuous optimization problems in finite-dimensional spaces. Variational convexity in infinite-dimensional spaces, which is studied here for the first time, is significantly more involved and requires the usage of powerful tools of geometric functional analysis together with variational analysis and generalized differentiation in Banach spaces.
