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Mat. Zametki, 2019, Volume 106, Issue 5, Pages 660–668 (Mi mz12141)  

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

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.

DOI: https://doi.org/10.4213/mzm12141

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English version:
Mathematical Notes, 2019, 106:5, 703–710

Bibliographic databases:

UDC: 519.853
Received: 03.08.2018

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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\by S.~I.~Dudov, M.~A.~Osiptsev
\paper A Formula for the Superdifferential of the Distance Determined by the Gauge Function to the Complement of a Convex Set
\jour Mat. Zametki
\yr 2019
\vol 106
\issue 5
\pages 660--668
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\transl
\jour Math. Notes
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\vol 106
\issue 5
\pages 703--710
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