Geodesic
Variational Analysis for the Bilateral Minimal Time Function
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 1029-105
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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.
Classification : 49J24, 49J52
Mots-clés : Bilateral minimal time function, Frechet subdifferential, singular subdifferential, normal cone 
@article{JCA_2017_24_3_JCA_2017_24_3_a17,
     author = {L. V. Nguyen},
     title = {Variational {Analysis} for the {Bilateral} {Minimal} {Time} {Function}},
     journal = {Journal of convex analysis},
     pages = {1029--105},
     year = {2017},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a17/}
}
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L. V. Nguyen. Variational Analysis for the Bilateral Minimal Time Function. Journal of convex analysis, Tome 24 (2017) no. 3, pp. 1029-105. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a17/