Geodesic
A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set
Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 660-668

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The distance determined by the Minkowski gauge function to the complement of a convex solid body in a finite-dimensional space is considered. The concavity of this distance function on a given convex set is proved, and a formula for its superdifferential at any interior point of this set is obtained. It is also proved that the distance function under consideration is directionally differentiable at the boundary points of the convex set, and formulas for its directional derivative are obtained.
Keywords: distance function, gauge function of a set, superdifferential, cone of possible directions, support function. 
@article{MZM_2019_106_5_a1,
     author = {S. I. Dudov and M. A. Osiptsev},
     title = {A {Formula} for the {Superdifferential} of the {Distance} {Determined} by the {Gauge} {Function} to the {Complement} of a {Convex} {Set}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {660--668},
     publisher = {mathdoc},
     volume = {106},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a1/}
}
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S. I. Dudov; M. A. Osiptsev. A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set. Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 660-668. http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a1/