Journal of Convex Analysis 32 (2025), No. 1, 107--118
Copyright Heldermann Verlag 2025
Lipschitz Differentiability of the Supporting Function from a Geometric Viewpoint, the Nearest and the Farthest Points
Maxim V. Balashov
Trapeznikov Institute of Control Sciences, Moscow, Russia
balashov73@mail.ru
Kamil Z. Biglov
Trapeznikov Institute of Control Sciences, Moscow, Russia
biglov.kz@phystech.su
We consider a supporting condition for a convex compact set in Rn. This condition is typical and it is closely related to the local Lipschitz differentiability of the supporting function. With the help of the considered condition we prove a local Lipschitz condition for supporting elements and for nearest and farthest points of a convex compact set. Some applications for numerical algorithms are discussed.
Keywords: Supporting function, subdifferential, supporting condition, nonsmooth analysis.
MSC: 49J52, 49J53, 52A20; 47H09.
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