Volume 26, 2020
|Number of page(s)||35|
|Published online||17 November 2020|
The minimal time function associated with a collection of sets*,**
Department of Natural Sciences, Hong Duc University,
Thanh Hoa, Vietnam
2 Department of Mathematics, Hangzhou Normal University, Hangzhou, P.R. China
*** Corresponding author: firstname.lastname@example.org
Accepted: 5 April 2020
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.
Mathematics Subject Classification: 49J52 / 49J53 / 90C46
Key words: Convex dynamics set / minimal time function / subdifferentials / normal cones / location problems
© EDP Sciences, SMAI 2020
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