论文标题
凸集的极端系统，并具有用于向量空间中凸线的应用的应用
Extremal Systems of Convex Sets with Applications to Convex Calculus in Vector Spaces
论文作者
论文摘要
在本文中，我们介绍并研究了在没有拓扑结构的矢量空间中凸集系统的极值概念。极端系统的表征是以凸极原理的形式获得的，这表明在通过代数核心表达的某些资格条件下凸出等效于凸间。获得的结果是通过变异几何方法应用的，以得出增强的计算规则，以供正常集合集合，凸面集值映射的代码词以及包括最佳值一个的扩展真实价值凸功能的扩展真实值凸功能的次级。这些平等类型的规则是根据任意向量空间中代数核心在精制资格条件下建立的。我们的新事态发展部分回答了一个问题，即我们可以在没有任何拓扑结构的情况下进行设置值和凸的分析。
In this paper we introduce and study the concept of set extremality for systems of convex sets in vector spaces without topological structures. Characterizations of the extremal systems of sets are obtained in the form of the convex extremal principle, which is shown to be equivalent to convex separation under certain qualification conditions expressed via algebraic cores. The obtained results are applied via a variational geometric approach to deriving enhanced calculus rules for normals to convex sets, coderivatives of convex set-valued mappings, and subgradients of extended-real-valued convex functions including the optimal value ones. These rules of the equality type are established under refined qualification conditions in terms of algebraic cores in arbitrary vector spaces. Our new developments partially answer the question on how far we can go with set-valued and convex analysis without any topological structure on the underlying spaces.
