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Sensitivity Properties of Parametric Nonconvex Evolution Inclusions with Application to Optimal Control Problems

  • Samir AdlyEmail author
  • Taron Zakaryan
Article
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Abstract

The main concern of this paper is to investigate sensitivity properties of parametric evolution systems of first order involving a general class of nonconvex functions. Using recent results on the stability of the subdifferentials, with respect to the Gamma convergence, of the associated sequence of subsmooth or semiconvex functions, we give some continuity properties of the solution set associated to these problems. The particular case of the parametric sweeping process involving uniformly subsmooth or uniformly prox-regular sets is studied in details. As an application, we study the sensitivity analysis of the generalized Bolza/Mayer problem governed by a nonsmooth dynamic of a sweeping process type.

Keywords

Sensitivity analysis Evolution inclusions Primal lower nice functions Semi-convex functions Sweeping process Prox-regular sets Bolza/Mayer problem Optimal control 

Mathematics Subject Classification (2010)

34A60 49J15 49J52 49J53 

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Notes

Acknowledgements

We are very grateful to the anonymous referee for his/her careful reading and relevant suggestions which considerably improved the paper.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.XLIM UMR-CNRS 7252Université de LimogesLimogesFrance

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