论文标题
超级函数的细分差异：连续和非连续设置之间来回移动
Subdifferential of the supremum function: Moving back and forth between continuous and non-continuous settings
论文作者
论文摘要
在本文中，我们为凸函数的点上的次分别开发了一般公式，该公式涵盖和统一紧凑的连续和非紧密连续设置。从非连续到连续的设置，我们通过一种基于紧凑的方法进行，这使我们遇到具有紧凑型索引集和上半连接型映射的问题，从而通过上层半连续的正则功能和延长的紧凑型索引集对超级分类的新特征产生了新的特征。从相反的意义上讲，我们通过使用原始数据来重写这些新的正规化功能的细分差异，这也导致我们对超级人的亚差异取得了新的结果。我们在上一节中提供了两个应用程序，这是第一个有关非convex Fenchel二元性的应用程序，第二个应用程序在凸半侵犯编程中建立Fritz-John和KKT条件的第二个应用程序。
In this paper we develop general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the non-continuous to the continuous setting, we proceed by a compactification-based approach which leads us to problems having compact index sets and upper semi-continuously indexed mappings, giving rise to new characterizations of the subdifferential of the supremum by means of upper semicontinuous regularized functions and an enlarged compact index set. In the opposite sense, we rewrite the subdifferential of these new regularized functions by using the original data, also leading us to new results on the subdifferential of the supremum. We give two applications in the last section, the first one concerning the nonconvex Fenchel duality, and the second one establishing Fritz-John and KKT conditions in convex semi-infinite programming.
