This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2020.20 (DV Cuong). Research of this author was partly supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research grant #15RT04, and by Australian Research Council under grant DP-190100555 (Mordukhovich). Research of this author was partly supported by the USA National Science Foundation under grant DMS-1716057 (MN Nam).
Convex functions, Mathematical analysis, Locally convex spaces, Vector spaces
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.
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
Van Cuong, D., Mordukhovich, B., Nam, N. M., & Wells, M. (2020). Convex Analysis of Minimal Time and Signed Minimal Time Functions. arXiv preprint arXiv:2010.10736.