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Journal of Convex Analysis 24 (2017), No. 3, 1029--1050
Copyright Heldermann Verlag 2017

Variational Analysis for the Bilateral Minimal Time Function

Luong V. Nguyen
Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warsaw, Poland


We derive formulas for the Fr\'echet (singular) subdiferentials of the bilateral minimal time function $T:\mathbb{R}^n \times \mathbb{R}^n \to [0,+\infty]$ associated with a system governed by differential inclusions. As a consequence, we give a connection between the Fr\'echet normals to the sub-level sets of $T$ and to its epigraph. Finally, we show that the Fr\'echet normal cones to the sub-level set of $T$ at a point $(\alpha,\beta)$ and to epi($T$) at $((\alpha,\beta),T(\alpha,\beta))$ have the same dimension.

Keywords: Bilateral minimal time function, Frechet subdifferential, singular subdifferential, normal cone.

MSC: 49J24, 49J52

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