
Journal of Convex Analysis 19 (2012), No. 3, 631669 Copyright Heldermann Verlag 2012 Geometric Conditions for Regularity in a TimeMinimum Problem with Constant Dynamics Vladimir V. Goncharov CIMAUE, Dep. de Matemática, Universidade de Évora, Rua Romăo Ramalho 59, 7000671 Évora, Portugal goncha@uevora.pt Fátima F. Pereira CIMAUE, Dep. de Matemática, Universidade de Évora, Rua Romăo Ramalho 59, 7000671 Évora, Portugal fmfp@uevora.pt [Abstractpdf] Continuing earlier research [``Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals'', J. Convex Analysis 18 (2011) 136] on local wellposedness of a timeminimum problem associated to a closed target set $C\subset H$ ($H$ is a Hilbert space) and a convex constant dynamics $F\subset H$ we study the Lipschitz (or, in general, H\"{o}lder) regularity of the (unique) point $\pi_{C}^{F}\left( x\right)$ in $C$ achieved from $x$ for a minimal time. As a consequence, smoothness of the value function is proved, and an explicit formula for its derivative is given. Keywords: Timeminimum problem, Hoelder continuity, proximal, Frechet subdifferential, Clarke subdifferential, duality mapping, curvature, proximal smoothness. MSC: 49J52, 49N15 [ Fulltextpdf (310 KB)] for subscribers only. 