论文标题
抽象细分运算符的变分特性
Variational properties of the abstract subdifferential operator
论文作者
论文摘要
摘要凸度通用通过考虑从任意定义的功能集中掌握的功能的上流来使经典凸度。这些称为抽象线性（抽象仿射）功能。本文的目的是研究抽象的细分。我们获得了有关此细分差异的计算的许多结果：求和和组成规则，并证明在某些合理条件下，细分是最大的抽象单调操作员。本文的另一个贡献是一个反例，表明两个抽象凸集之间的分离定理通常不正确。缺乏分离结果到抽象凸度的情况是基于抽象凸度的数值方法发展的障碍之一。
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to study the abstract subdifferential. We obtain a number of results on the calculus of this subdifferential: summation and composition rules, and prove that under some reasonable conditions the subdifferential is a maximal abstract monotone operator. Another contribution of this paper is a counterexample that demonstrates that the separation theorem between two abstract convex sets is generally not true. The lack of the extension of separation results to the case of abstract convexity is one of the obstacles in the development of abstract convexity based numerical methods.
