In this paper, we develop an enhanced version of the catching-up algorithm for sweeping processes through an appropriate concept of approximate projection. We establish some properties of this notion of approximate projection. Then, under suitable assumptions, we show the convergence of the enhanced catching-up algorithm for prox-regular, subsmooth, and merely closed sets. Finally, we briefly discuss some efficient numerical methods for obtaining approximate projections. Our results recover classical existence results in the literature and provide new insights into the numerical simulation of sweeping processes.

中文翻译：

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具有莫罗扫掠过程近似投影的追赶算法

在本文中，我们通过适当的近似投影概念开发了用于扫掠过程的追赶算法的增强版本。我们建立了近似投影概念的一些属性。然后，在适当的假设下，我们展示了针对 prox-regular、次平滑和纯闭集的增强追赶算法的收敛性。最后，我们简要讨论一些获得近似投影的有效数值方法。我们的结果恢复了文献中的经典存在结果，并为扫掠过程的数值模拟提供了新的见解。