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Nonconvex Sweeping Process with a Moving Set Depending on the State

Abstract

Recently, a great advance has been made in the study of sweeping process variational inequalities with the papers (Chemetov, Monteiro Marques Set-Valued Anal. 15, 209–221, 2007 Castaing et al. J. Nonlinear Convex Anal. 10, 1–20, 2009 Haddad J. Optim. Theory Appl. 159, 386–398, 2013 Azzam-Laouir et al. Set-Valued Var. Anal. 22, 271–283, 2014 where, for a prox-regular moving set depending on both the time and the state, several existence results are provided. Those authors also studied the case where such a differential inclusion is perturbed by multimapping. The present paper establishes the existence of solutions for such perturbed differential inclusions in some context not considered in the previous papers.

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Correspondence to Lionel Thibault.

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Noel, J., Thibault, L. Nonconvex Sweeping Process with a Moving Set Depending on the State. Vietnam J. Math. 42, 595–612 (2014). https://doi.org/10.1007/s10013-014-0109-8

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  • DOI: https://doi.org/10.1007/s10013-014-0109-8

Keywords

  • Differential inclusion
  • Sweeping process
  • Normal cone
  • Prox-regular set
  • Subdifferential

Mathematics Subject Classifications (2010)

  • 34A60
  • 49J52
  • 49J24
  • 49J53