The polyhedral approximation of a positively homogeneous (and, in general, nonconvex)
function on a unit sphere is investigated. Such a function is presupporting (ie, its convex hull …

The problem of polyhedral approximation of a multidimensional ball is considered. It is well
known that the norm of the f-vector (the maximum number of faces of all dimensions) of an …

The estimate refinement method for the polyhedral approximation of convex compact bodies
is analyzed. When applied to convex bodies with a smooth boundary, this method is known …

The internal polyhedral approximation of convex compact bodies with twice continuously
differentiable boundaries and positive principal curvatures is considered. The growth of the …

A class of iterative methods—filling methods—for polyhedral approximation of convex
compact bodies is introduced and studied. In contrast to augmentation methods, the vertices …

Given a convex body, the finite-dimensional problem is considered of minimizing the ratio of
its circumradius to its inradius (in an arbitrary norm) by choosing a common center of the …

The estimate refinement method for the polyhedral approximation of convex compact bodies
is considered. In the approximation of convex bodies with a smooth boundary, this method is …

The finite-dimensional problem of the best approximation (in the Hausdorff metric) of a
convex body by a ball of arbitrary norm with a fixed radius is considered. The stability and …

A duality theory is developed to describe iterative methods for polyhedral approximation of
convex bodies. The various types of approximation problems requiring the application of the …

A comparative analysis of the complexity of approaches to the approximation of convex
compact bodies by double description polytopes is provided as applied to a ball. A …