
Journal of Convex Analysis 24 (2017), No. 3, 10291050 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, 00656 Warsaw, Poland luonghdu@gmail.com [Abstractpdf] 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 sublevel sets of $T$ and to its epigraph. Finally, we show that the Fr\'echet normal cones to the sublevel 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 [ Fulltextpdf (173 KB)] for subscribers only. 