论文标题
具有非线性缩放的透视功能
Perspective Functions with Nonlinear Scaling
论文作者
论文摘要
一个函数的经典视角是将凸函数转换为相对于辅助缩放变量共同凸的构造。在应用分析的几个领域的应用中，我们研究了该结构的扩展，其中缩放变量被非线性术语代替。我们的构造位于本地凸空间的一般环境中，它在基础函数的广泛假设下产生了较低的半连续凸函数。建立了各种凸 - 分析特性，并得出了封闭形式的表达式。提出了几种申请。
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.
