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Journal of Convex Analysis 27 (2020), No. 1, 313--333
Copyright Heldermann Verlag 2020

Subdifferentiation of the Infimal Convolution and Minimal Time Problems

Abderrahim Hantoute
Center of Mathematical Modeling, Universidad de Chile, Santiago, Chile

Taron Zakaryan
Université Paris Nanterre, 200 Av. de la République, 92000 Nanterre, France

We investigate in the Banach setting (not necessarily reflexive) first-order variations of the infimal convolution of fairly general functions. We characterize different subdifferentials and differentiability concepts of this infimal convolution by means of the corresponding subdifferentials and differentiability concepts, respectively, of data functions, at points where the infimal convolution is attained, well-posed, or strongly attained. Next, we apply these results to study the (sub)differentiability of minimal time functions associated with constant dynamics satisfying appropriate interiority conditions.

Keywords: Infimal convolution, generalized subdifferentials, differentiability, minimal time function.

MSC: 49J50, 90C31, 93B03.

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