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Journal of Convex Analysis 31 (2024), No. 1, 059--074
Copyright Heldermann Verlag 2024

Perturbed Degenerate State-Dependent Sweeping Processes with Convex and Nonconvex Sets

Diana Narváez
(1) Dep. de Ingeniería Matemática, Universidad de Chile, Santiago, Chile
(2) Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

Emilio Vilches
Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Rancagua, Chile

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.

Keywords: Sweeping Processes, normal cone, mirror descent method, subsmooth sets, Moreau-Yosida regularization.

MSC: 34G25, 49J52, 49J53.

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