| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 93 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2020017 | |
| Published online | 17 November 2020 | |
The minimal time function associated with a collection of sets*,**
1
Department of Natural Sciences, Hong Duc University,
Thanh Hoa, Vietnam
2
Department of Mathematics, Hangzhou Normal University,
Hangzhou, P.R. China
*** Corresponding author: qxlxajh@163.com
Received:
24
May
2019
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.