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Numerical Method for a Controlled Sweeping Process with Nonsmooth Sweeping Set

Author

Listed:
  • Chadi Nour

    (Lebanese American University)

  • Vera Zeidan

    (Michigan State University)

Abstract

The numerical method developed in Nour and Zeidan (IEEE Control Syst. Lett. 6:1190-1195, 2022) via the exponential penalization technique for optimal control problems involving sweeping processes with sweeping set C generated by one smooth function, is generalized in this paper to the case where C is nonsmooth. That is, C is the intersection of a finite number (greater than one) of sublevel sets of smooth functions. The change from one to greater than one generating smooth functions is quite challenging. Indeed, while in the latter case C could be reformulated as being generated by one function, however, this function is only Lipschitz, and hence, the method established for one generating smooth function is not applicable to this framework. Therefore, this general setting requires a new approach, which represents the novelty of this paper.

Suggested Citation

  • Chadi Nour & Vera Zeidan, 2024. "Numerical Method for a Controlled Sweeping Process with Nonsmooth Sweeping Set," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1385-1412, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02470-x
    DOI: 10.1007/s10957-024-02470-x
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    References listed on IDEAS

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    1. MdR Pinho & M. M. A. Ferreira & G. Smirnov, 2020. "Optimal Control with Sweeping Processes: Numerical Method," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 845-858, June.
    2. Xing-Si Li & Shu-Cherng Fang, 1997. "On the entropic regularization method for solving min-max problems with applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(1), pages 119-130, February.
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