Abstract

We derive formulas for the Fréchet (singular) subdiferentials of the bilateral minimal time function T:Rn×Rn→[0,+∞]T:\mathbb{R}^n \times \mathbb{R}^n \to [0,+\infty] associated with a system governed by differential inclusions. As a consequence, we give a connection between the Fréchet normals to the sub-level sets of TT and to its epigraph. Finally, we show that the Fréchet normal cones to the sub-level set of TT at a point (α,β)(\alpha,\beta) and to epi(TT) at ((α,β),T(α,β))((\alpha,\beta),T(\alpha,\beta)) have the same dimension.

Author information

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

Luong V. Nguyen

Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland

luonghdu@gmail.com

Keywords

  • Bilateral minimal time function
  • Fréchet subdifferential
  • singular subdifferential
  • normal cone

Mathematics Subject Classification

49J24, 49J52

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Suggested citation

L. V. Nguyen. “Variational Analysis for the Bilateral Minimal Time Function.” Journal of Convex Analysis 24 (2017), No. 3, 1029–1050. https://doi.org/10.68381/jca24062

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.