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 set-valued 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.