论文标题
设置连接及其应用：教程
Set-Convergence and Its Application: A Tutorial
论文作者
论文摘要
优化问题，广义方程式以及许多其他变异问题总是会导致集合和集合值映射及其近似值的分析。我们回顾了集合连接的核心概念，并解释了其在定义集合之间邻近概念中的作用，尤其是对于功能的题词和集合值映射的图表。该发展导致了一种近似理论，用于优化问题和广义方程式，对算法的构建产生了深远的影响。我们还介绍了设定连接在变异几何形状中的作用，并在最佳条件下应用于应用程序。示例说明了集合在稳定性分析，错误分析，算法的构建，统计估计和概率理论中的重要性。
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence and explain its role in defining a notion of proximity between sets, especially for epigraphs of functions and graphs of set-valued mappings. The development leads to an approximation theory for optimization problems and generalized equations with profound consequences for the construction of algorithms. We also introduce the role of set-convergence in variational geometry and subdifferentiability with applications to optimality conditions. Examples illustrate the importance of set-convergence in stability analysis, error analysis, construction of algorithms, statistical estimation, and probability theory.
