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Matematicheskie Zametki, 2019, Volume 106, Issue 5, Pages 660–668
DOI: https://doi.org/10.4213/mzm12141
(Mi mzm12141)
 

A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set

S. I. Dudov, M. A. Osiptsev

Saratov State University
References:
Abstract: 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.
Received: 03.08.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 5, Pages 703–710
DOI: https://doi.org/10.1134/S000143461911004X
Bibliographic databases:
Document Type: Article
UDC: 519.853
Language: Russian
Citation: 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”, Mat. Zametki, 106:5 (2019), 660–668; Math. Notes, 106:5 (2019), 703–710
Citation in format AMSBIB
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\pages 660--668
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