Subgradients of Minimal Time Functions without Calmness

TL;DR

This paper advances the variational analysis of minimal time functions by deriving new generalized differentiation results, especially concerning their singular and limiting subdifferentials, under less restrictive assumptions.

Contribution

It provides novel results on the subdifferentials of minimal time functions without requiring calmness assumptions, broadening the scope of variational analysis in this area.

Findings

New formulas for subdifferentials of minimal time functions

Relaxation of assumptions needed for subdifferential analysis

Enhanced understanding of nonsmooth variational properties

Abstract

In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of research by providing new results on generalized differentiation of this class of functions, relaxing assumptions imposed on the functions and sets involved for the results. In particular, we focus on the singular subdifferential and the limiting subdifferential of this class of functions.