State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches

Samir Adly (), Monica G. Cojocaru () and Ba Khiet Le ()
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Samir Adly: Université de Limoges
Monica G. Cojocaru: University of Guelph
Ba Khiet Le: Ton Duc Thang University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 2, No 16, 932-948

Abstract: 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.

Keywords: Asymptotic analysis; State-dependent sweeping processes; Quasi-variational inequalities; Derivative-free algorithm; 28B05; 34A36; 34A60; 49J52; 49J53; 93D20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02485-4

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