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Journal of Convex Analysis 20 (2013), No. 4, 1095--1112
Copyright Heldermann Verlag 2013

Proximal Subdifferential of the Bilateral Minimal Time Function and some Regularity Applications

Chadi Nour
Dept. of Computer Science and Mathematics, Lebanese American University, Byblos Campus -- P.O. Box 36, Byblos, Lebanon

We derive a formula for the proximal subdifferential of the bilateral minimal time function in the linear case. As a consequence, we prove some new regularity properties for this function, essentially, we provide suitable weak controllability assumption under which its epigraph is locally φ0-convex.

Keywords: Bilateral and unilateral minimal time function, linear control system, phi-convexity, proximal analysis, nonsmooth analysis.

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