The concept of penumbra of a convex set with respect to another convex set was introduced by Rockafellar (1970). We study various geometric and topological properties of penumbras, their role in proper and strong separation of convex sets, and their relation to polyhedra and M-decomposable sets.

中文翻译：

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半影和凸集的分离

Rockafellar (1970) 引入了凸集相对于另一个凸集的半影的概念。我们研究了半影的各种几何和拓扑特性，它们在适当和强分离凸集中的作用，以及它们与多面体和 M 可分解集的关系。