Subdifferential properties for a class of minimal time functions with moving target sets in normed spaces

Abstract

In a normed vector space, we study the minimal time function determined by a moving target set and a differential inclusion, where the set-valued mapping involved has constant values of a bounded closed convex set U. After establishing a characterization of ϵ-subdifferential of the minimal time function, we obtain that the limiting subdifferential of the minimal time function is representable by virtue of the corresponding normal cones of sublevel sets of the function and level or sublevel sets of the support function of U. The known results require the set U to have the origin as an interior point and the target set is a fixed set.

Keywords:

• minimal time function
• subdifferential
• normal cone
• moving target set

AMS Subject Classifications:

• 49L20
• 35D05

Acknowledgements

This work was partially supported by National Natural Science Foundation of China (No. 10701059) and Scientific Research Fund of SiChuan Provincial Education Department. We thank the referee for helpful suggestions.