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State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches

Author

Listed:
  • Samir Adly

    (Université de Limoges)

  • Monica G. Cojocaru

    (University of Guelph)

  • Ba Khiet Le

    (Ton Duc Thang University)

Abstract

In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data.

Suggested Citation

  • Samir Adly & Monica G. Cojocaru & Ba Khiet Le, 2024. "State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 932-948, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02485-4
    DOI: 10.1007/s10957-024-02485-4
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    References listed on IDEAS

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    1. Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
    2. NESTEROV, Yurii & SCRIMALI, Laura, 2011. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Reprints CORE 2357, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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