Catching-Up Algorithm with Approximate Projections for Moreau’s Sweeping Processes

Juan Guillermo Garrido () and Emilio Vilches ()
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Juan Guillermo Garrido: Universidad de Chile
Emilio Vilches: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 4, 1160-1187

Abstract: Abstract 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.

Keywords: Sweeping process; Differential inclusions; Approximate projections; 34A60; 49J52; 34G25; 49J53 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02407-4

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