Catching-up Algorithm with Approximate Projections for Moreau's Sweeping Processes

2023/08/16 by Juan Guillermo Garrido, Garrido, Juan Guillermo, Emilio Vilches +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2308.08093

openalex publication_date 2023/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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