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In this paper, we investigate the asymptotic properties of a particular classof state-dependent sweeping processes. While extensive research has beenconducted on the existence and uniqueness of solutions for sweeping processes,there is a scarcity of studies addressing their behavior in the limit of largetime. Additionally, we introduce novel algorithms designed for the resolutionof quasi-variational inequalities. As a result, we introduce a newderivative-free algorithm to find zeros of nonsmooth Lipschitz continuousmappings with a linear convergence rate. This algorithm can be effectively usedin nonsmooth and nonconvex optimization problems that do not possessnecessarily second-order differentiability conditions of the data.

State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches