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Journal of Convex Analysis 26 (2019), No. 1, 189--200
Copyright Heldermann Verlag 2019

Subgradients of Minimal Time Functions without Calmness

Nguyen Mau Nam
Fariborz Maseeh Dept. of Mathematics and Statistics, Portland State University, PO Box 751, Portland, OR 97207, U.S.A.

Dang Van Cuong
Dept. of Mathematics, Duy Tan University, Da Nang, Vietnam

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.

Keywords: Minimal time function, epsilon-Frechet subdifferential, limiting subdifferential, singular subdifferential, calmness.

MSC: 49J52, 49J53, 90C31

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