Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


compact convex set

On a Approximate Solution of the Problem of Aspherical Convex Compact Set

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution. At each step of the iterative process it is required to solve the problem of convex programming, target function of which is the difference between the radius of a circumscribed sphere, and scalable, with some positive factor, the radius of the inscribed sphere.

The Characteristic of Stability of the Solution in the Problem of Convex Compact Set Asphericity

We consider the problem of stability of the solution in the problem of asphericity of a convex set with respect to the error of defining the compact set. It is shown that the optimal value of the criterion function (an asphericity indicator) is stable. Properties of the setvalued mapping, that puts to a convex compact compact set the centers of its asphericity are also investigated. It is proved that this mapping is semicontinious from above everywhere in the space of convex compact sets.