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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

dnarvaez@dim.uchile.cl

Emilio Vilches

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

emilio.vilches@uoh.cl

Keywords

  • Sweeping Processes
  • normal cone
  • mirror descent method
  • subsmooth sets
  • Moreau-Yosida regularization

Mathematics Subject Classification

34G25, 49J52, 49J53

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Suggested citation

D. Narváez, E. Vilches. “Perturbed Degenerate State-Dependent Sweeping Processes with Convex and Nonconvex Sets.” Journal of Convex Analysis 31 (2024), No. 1, 59–74. https://doi.org/10.68381/jca31005

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