Geodesic
Optimal growth order of the number of vertices and facets in the class of Hausdorff methods for polyhedral approximation of convex bodies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1018-1031

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The internal polyhedral approximation of convex compact bodies with twice continuously differentiable boundaries and positive principal curvatures is considered. The growth of the number of facets in the class of Hausdorff adaptive methods of internal polyhedral approximation that are asymptotically optimal in the growth order of the number of vertices in approximating polytopes is studied. It is shown that the growth order of the number of facets is optimal together with the order growth of the number of vertices. Explicit expressions for the constants in the corresponding bounds are obtained. 
@article{ZVMMF_2011_51_6_a4,
     author = {R. V. Efremov and G. K. Kamenev},
     title = {Optimal growth order of the number of vertices and facets in the class of {Hausdorff} methods for polyhedral approximation of convex bodies},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1018--1031},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a4/}
}
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R. V. Efremov; G. K. Kamenev. Optimal growth order of the number of vertices and facets in the class of Hausdorff methods for polyhedral approximation of convex bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1018-1031. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a4/