SIAM Journal on Optimization, Volume 31, Issue 2, Page 1330-1351, January 2021.
We obtain new properties and formulas for the horizon map and graphical convergence for set-valued maps. We calculate horizon maps and establish the graphical convergence of various important maps from variational analysis. We also establish the continuity of several operations with set-valued maps. We compare these notions with similar ones from the literature. We also study the notion of total graphical convergence. Finally, to illustrate the usefulness of the developed tools, we employ them to study the stability, asymptotic behavior, and existence of solutions of generalized equations. Our results contribute to the asymptotic analysis and convergence theory for set-valued maps.

中文翻译：

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重新审视地平线地图和图形融合

SIAM优化杂志，第31卷，第2期，第1330-1351页，2021年1月。
我们获得了水平图的新属性和公式以及集值图的图形收敛。我们计算水平图，并通过变分分析建立各种重要图的图形收敛性。我们还使用集合值映射来建立多个操作的连续性。我们将这些概念与文献中的类似概念进行比较。我们还研究了整体图形收敛的概念。最后，为了说明所开发工具的实用性，我们使用它们来研究稳定性，渐近行为和广义方程解的存在性。我们的结果有助于集值映射的渐近分析和收敛理论。