Minimal Time Functions and the Smallest Intersecting Ball Problem with Unbounded Dynamics

The minimal time function associated with a collection of sets

“…, ∀x ∈ X. We are now going to present some basic properties of the minimal time function T U ,Ω by carefully extending analogous properties of the usual minimal time function which can be found in, e.g., [3,9,13,23,26,30].…”

“…In [31], Sun and He proved the Fréchet and the proximal subdifferential formulas at points outside the target without using any calmness condition. For other paper deals with computing general differentiation of classical minimal time function, we refer the reader, to, e.g., [2,3,13,22,23,26,29,30].…”

“…Variational analysis and generalized differentiations of the minimal time function associated with a convex dynamics set, which contains the origin in its interior, in a Hilbert space was initially studied by Colombo and Wolenski in [8,9]. Since then, the minimal time function has been extensively studied by many researchers in various ways and for different purposes; see, e.g., [2,3,7,13,17,18,22,23,26,29,31]. In [17], He and Ng studied generalized differentiations of the minimal time function in Banach spaces.…”

“…Results presented in the above-mentioned papers were extended and improved in [22,23] by Mordukhovich and Nam and then were further extended to the context of Hausdorff topological vector spaces in [2,3] by Bounkhel. We also refer the reader to [29,31] for the study of subdifferentials of the minimal time function without calmness assumptions. Applications of variational analysis and generalization differentiations of the minimal time function to generalized Sylvester problems and to generalized Fermat -Terricelli problems were presented in [23][24][25][26][27][28]30] and references therein. For variational analysis and applications of the function T F Ω when F is a subset of the unit sphere, we refer the reader to [13][14][15].…”

Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

“…The readers are referred to [4,5,8,9,12,14,15,17,19,21,22,25,26] and the references therein for the study of the minimal time function as well as its specification to the case of the distance function.…”