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

Author

Listed:
  • Juan Guillermo Garrido

    (Universidad de Chile)

  • Emilio Vilches

    (Universidad de O’Higgins)

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.

Suggested Citation

  • Juan Guillermo Garrido & Emilio Vilches, 2024. "Catching-Up Algorithm with Approximate Projections for Moreau’s Sweeping Processes," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1160-1187, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02407-4
    DOI: 10.1007/s10957-024-02407-4
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    References listed on IDEAS

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    1. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
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