Geodesic
On polyhedral approximations in an $n$-dimensional space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1695-1701

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The polyhedral approximation of a positively homogeneous (and, in general, nonconvex) function on a unit sphere is investigated. Such a function is presupporting (i.e., its convex hull is the supporting function) for a convex compact subset of $R^n$. The considered polyhedral approximation of this function provides a polyhedral approximation of this convex compact set. The best possible estimate for the error of the considered approximation is obtained in terms of the modulus of uniform continuous subdifferentiability in the class of a priori grids of given step in the Hausdorff metric. 
@article{ZVMMF_2016_56_10_a0,
     author = {M. V. Balashov},
     title = {On polyhedral approximations in an $n$-dimensional space},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1695--1701},
     publisher = {mathdoc},
     volume = {56},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a0/}
}
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M. V. Balashov. On polyhedral approximations in an $n$-dimensional space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1695-1701. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a0/