论文标题
重新访问Rockafellar的定理，该定理在凸图的相对内饰上使用凸广义分化的应用
Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
论文作者
论文摘要
在本文中，我们通过Rockafellar重新访问定理，以代表凸集设置值映射的相对内部，以其域和功能值的相对内部表示。然后，我们应用此定理来提供一种简单的方法来证明在有限维度中的设置值映射和非平滑函数的广义分化的许多计算规则。这些结果通过替换在域和/或范围上具有资格的图表上的相对内部资格来改善[14]中的结果。
In this paper we revisit a theorem by Rockafellar on representing the relative interior of the graph of a convex set-valued mapping in terms of the relative interior of its domain and function values. Then we apply this theorem to provide a simple way to prove many calculus rules of generalized differentiation of set-valued mappings and nonsmooth functions in finite dimensions. These results improve upon those in [14] by replacing the relative interior qualifications on graphs with qualifications on domains and/or ranges.
