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Reduction of state dependent sweeping process to unconstrained differential inclusion

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Abstract

In this article we discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets. We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state dependent sweeping process with unbounded perturbations. The perturbations are not required to be convex valued.

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Acknowledgments

We thank the referees for their careful reading which allowed us to improve the presentation of the paper.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Jijel, B.P. 98, Jijel, Algérie

    Tahar Haddad

  2. Département de Mathématiques, Université Montpellier II, 34095 , Montpellier Cedex 5, France

    Ilyas Kecis & Lionel Thibault

Authors
  1. Tahar Haddad
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  2. Ilyas Kecis
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  3. Lionel Thibault
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Correspondence to Tahar Haddad.

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Haddad, T., Kecis, I. & Thibault, L. Reduction of state dependent sweeping process to unconstrained differential inclusion. J Glob Optim 62, 167–182 (2015). https://doi.org/10.1007/s10898-014-0220-0

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  • DOI: https://doi.org/10.1007/s10898-014-0220-0

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