The minimal time function associated with a collection of sets
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 93.

We define the minimal time function associated with a collection of sets which is motivated by the optimal time problem for nonconvex constant dynamics. We first provide various basic properties of this new function: lower semicontinuity, principle of optimality, convexity, Lipschitz continuity, among others. We also compute and estimate proximal, Fréchet and limiting subdifferentials of the new function at points inside the target set as well as at points outside the target. An application to location problems is also given.

DOI : 10.1051/cocv/2020017
Classification : 49J52, 49J53, 90C46
Mots-clés : Convex dynamics set, minimal time function, subdifferentials, normal cones, location problems 
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     title = {The minimal time function associated with a collection of sets},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
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Nguyen, Luong V.; Qin, Xiaolong. The minimal time function associated with a collection of sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 93. doi : 10.1051/cocv/2020017. http://www.numdam.org/articles/10.1051/cocv/2020017/

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This paper was supported by the National Natural Science Foundation of China under Grant No.11401152.

LVN was supported by the Research Fund for International Young Scientists from NNSFC under Grant No.11850410438 and China Postdoctoral Science Foundation under Grant No. 2017M6200421.