Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 3, 1029--1050Copyright 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 luonghdu@gmail.com [Abstract-pdf] 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 [ Fulltext-pdf  (173  KB)] for subscribers only.