论文标题
部分可观测时空混沌系统的无模型预测
Resolvent and Proximal Compositions
论文作者
论文摘要
我们介绍了线性运算符和设定值操作员之间的单调性保留操作，以及近端组合物，线性操作员和函数之间的凸功能操作。这两个操作是通过以下事实联系在一起的：在温和的假设下，凸函数的近端组成的亚不同是其亚差异的分解组成。结果证明了分解和近端组成封装已知概念，例如分解和近端平均值，以及与平衡问题分析有关的新操作。建立了这些组成的大量属性，并讨论了几种实例。提出了单调包含和凸优化问题的放松的应用。
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function. The two operations are linked by the fact that, under mild assumptions, the subdifferential of the proximal composition of a convex function is the resolvent composition of its subdifferential. The resolvent and proximal compositions are shown to encapsulate known concepts, such as the resolvent and proximal averages, as well as new operations pertinent to the analysis of equilibrium problems. A large core of properties of these compositions is established and several instantiations are discussed. Applications to the relaxation of monotone inclusion and convex optimization problems are presented.
