2024· Journal of Convex Analysis· Vol 31, pp. 59-74· 2 citations· ⚡ 1 influential· 49 references
Abstract
We prove by means of the Moreau-Yosida regularization an existence result for perturbed degenerate state-dependent sweeping processes with convex and nonconvex moving sets. The moving sets vary in a Lipschitz continuous way with respect to the truncated Hausdorff distance. The theoretical results are applied to obtain the well-posedness for the online mirror descent method. The novelty of this work lies in the introduction of new local arguments for the Moreau-Yosida regularization that allow us to obtain the existence of solutions in small intervals and then pass to any interval.
In a separable Hilbert space, we consider a sweeping process with perturbation. The values of the moving set are prox-regular sets dependent on time and state. The variation of the moving set is controlled in the state in a Lipschitz way and in time by a positive Radon measure. The perturbation is the sum of two multiv...
A. Tolstonogov· Journal of Convex Analysis· 0 citations
Motivated by the numerical resolution of stochastic optimal control problems, particularly those involving nonlinear dynamics, we investigate the convergence properties of the Douglas-Rachford splitting algorithm in a nonconvex and infinite-dimensional setting. We introduce an extension of the method that applies when...
François Caffier, P. Malisani, Laurent Pfeiffer· 0 citations
In an infinite-dimensional Hilbert space, we investigate a method for finding a solution of a variational inequality induced by an inverse strongly monotone set-valued mapping. Our results are established in the presence of summable and nonsummable computational errors. We show that our algorithm generates a good appro...
We disprove a conjecture of Davis, Drusvyatskiy, and Jiang (2026) that subdifferential regularity can be removed from the generic guarantee of convergence to local minimizers for stochastic subgradient methods. We construct a globally Lipschitz, coercive, semialgebraic function in two dimensions for which the method co...
Sweeping processes, introduced by J. J. Moreau, have been studied significantly in recent years due to their interesting applications in practice. However, most of the researches use the global Hausdorff distance to describe the movement of the moving set, which is probably not satisfied for unbounded cases. In this pa...
