Set-Valued and Variational Analysis

, Volume 26, Issue 3, pp 581–606 | Cite as

Infimal Convolution and Optimal Time Control Problem I: Fréchet and Proximal Subdifferentials

  • Grigorii E. IvanovEmail author
  • Lionel Thibault


We consider a general minimal time problem with a convex constant dynamics and a lower semicontinuous extended real-valued target function defined on a Banach space. If the target function is the indicator function of a closed set, this problem is a minimal time problem for a target set, studied previously in particular by Colombo, Goncharov and Mordukhovich. We investigate several properties of the Fréchet and proximal subdifferentials for the infimum time function. Also explicit expressions of the above mentioned subdifferentials as well as various directional derivatives are obtained. We provide some examples to show the essentiality of assumptions of our theorems.


Fréchet subdifferential Proximal subdifferential Dini directional derivative Generalized directional derivative Minimal time function Minimal time projection Infimal convolution 

Mathematics Subject Classification (2010)

49J52 46N10 58C20 28B20 


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellier Cedex 05France
  3. 3.Centro de Modelamiento MatematicoUniversidad de ChileSantiagoChile

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