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Convex Analysis of Minimal Time and Signed Minimal Time Functions

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arxiv 2010.10736 v1 pith:LUEE7ANW submitted 2020-10-21 math.OC

Dang Van Cuong , Boris Mordukhovich , Nguyen Mau Nam , Mike Wells This is my paper · ORCID
classification math.OC
keywords functionsminimaltimesignedclassconvexdistanceobtained
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In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets with respect to constant dynamics. Then we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.

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