asphericity

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

Authors: Dudov S. I., Mesheryakova Е. А.

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.

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

Authors: Dudov S. I., Mesheryakova Е. А.

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.