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. It is shown that this auxiliary problem, in case of convex compact, and the ball of the used norm being polyhedral, can be reduced to a linear programming problem.