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

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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.

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Acknowledgements

This work was supported by the Center for Mathematical Modeling (CMM) and ANID-Chile under BASAL funds for Center of Excellence FB210005, Fondecyt Regular 1200283, Fondecyt Regular 1240120 and Fondecyt Exploración 13220097. We also acknowledge ECOS-Anid Project PC23E11 and MathAmsud Project 23-MATH-17. The authors would like to express their sincere gratitude to the anonymous referees for their valuable discussions and insightful suggestions. Their contributions have played a vital role in enhancing the overall quality of this manuscript.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

    Juan Guillermo Garrido

  2. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    Emilio Vilches

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  1. Juan Guillermo Garrido
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  2. Emilio Vilches
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Correspondence to Emilio Vilches.

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Communicated by Giovanni Colombo.

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Garrido, J.G., Vilches, E. Catching-Up Algorithm with Approximate Projections for Moreau’s Sweeping Processes. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02407-4

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