Geodesic
A Nonlinear φ0-Convexity Result for the Bilateral Minimal Time Function
Journal of convex analysis, Tome 28 (2021) no. 1, pp. 81-102
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For a nonlinear control system, we derive a ϕ0-convexity result for the epigraph of the bilateral minimal time function. This extends the main result in a previous publication of the second author [Proximal subdifferential of the bilateral minimal time function and some regularity applications, J. Convex Analysis 20 (2013) 1095--1112], which discussed the linear case.
Classification : 49N60, 49J52, 34A60
Mots-clés : Bilateral minimal time function, nonlinear control system, ϕ0-convexity, proximal analysis, nonsmooth analysis 
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     author = {S. Chamoun and C. Nour},
     title = {A {Nonlinear} {\ensuremath{\varphi}\protect\textsubscript{0}-Convexity} {Result} for the {Bilateral} {Minimal} {Time} {Function}},
     journal = {Journal of convex analysis},
     pages = {81--102},
     year = {2021},
     volume = {28},
     number = {1},
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S. Chamoun; C. Nour. A Nonlinear φ0-Convexity Result for the Bilateral Minimal Time Function. Journal of convex analysis, Tome 28 (2021) no. 1, pp. 81-102. http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a7/