Subdifferential properties of a perturbed minimal time function in normed spaces

Abstract

In a normed space, we study the perturbed minimal time function determined by a bounded closed convex set and a proper lower semicontinuous function. It covers the perturbed distance function as a special case. In particular, we show that the ε-subdifferential and the limiting subdifferential of the perturbed minimal time function are representable by virtue of corresponding subdifferential of the associated function and the support function of the constraint set.

Keywords:

• Pertubed minimal time function
• ε-subdifferential
• limiting subdifferential

Maths:

• 49J52
• 49J53

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China [11201324], Fok Ying Tung Education Foundation [141114], Sichuan Province Nature Foundation of China [2022NSFSC1852]  .