论文标题
平静和微积分：两个基本模式
Calmness and Calculus: Two Basic Patterns
论文作者
论文摘要
我们建立了两种类型的估计值的估计值，这些估计值是设定值映射的概述，这些映射具有两种基本模式的本质，观察到了一堆微积分规则。这些估计还说明了这两个模式伴随的基本假设的作用，一方面是平静，另一方面（模糊）内在的平静*。之后，我们研究了（内部）平静的各种概念之间的关系和足够条件。应用上述估计值，以恢复针对切线和正常的几种突出的微积分规则，以及边缘函数和组成的广义衍生物，以及在轻度条件下的笛卡尔产物。我们认为，我们增强的方法将总体广义的演算置于其他一些眼中。提出了我们发现的某些应用，这些应用是为最小值优化问题以及与最近引入的半齿性*属性相关的微积分所必需的最佳条件。
We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed troughout the pile of calculus rules. These estimates also illustrate the role of the essential assumptions that accompany these two patters, namely calmness on the one hand and (fuzzy) inner calmness* on the other. Afterwards, we study the relationship between and sufficient conditions for the various notions of (inner) calmness. The aforementioned estimates are applied in order to recover several prominent calculus rules for tangents and normals as well as generalized derivatives of marginal functions and compositions as well as Cartesian products of set-valued mappings under mild conditions. We believe that our enhanced approach puts the overall generalized calculus into some other light. Some applications of our findings are presented which exemplary address necessary optimality conditions for minimax optimization problems as well as the calculus related to the recently introduced semismoothness* property.
