State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Adly, Samir, Cojocaru, Monica G, Ba Khiet Le
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.11.2023
Subjects
Algorithms
Asymptotic properties
Sweeping
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Summary: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.
ISSN:2331-8422