用于Moreau扫掠过程的带近似投影的追赶算法
Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes
AI总结：
针对Moreau扫掠过程，提出带近似投影的增强追赶算法，证明其在多类集合上的收敛性并给出数值实现方法。
摘要：
本文通过适当的近似投影概念，开发了扫掠过程追赶算法的增强版本。我们建立了这种近似投影概念的若干性质。随后，在适当假设下，证明了增强型追赶算法对prox-正则集、次光滑集以及仅闭集的收敛性。最后，讨论了获取近似投影的高效数值方法。我们的结果恢复了文献中的经典存在性结论，并为扫掠过程的数值模拟提供了新的见解。
英文摘要：
In this paper, we develop an enhanced version of the catching-up algorithm for sweeping processes through an appropriate concept of approximate projections. 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 discuss efficient numerical methods for obtaining approximate projections. Our results recover classical existence results in the literature and provide new insight into the numerical simulation of sweeping processes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
