Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons

We study the problem of finding the optimal location of a set of moving figures within the boundaries of a given convex set (arena) on the plane. The optimality criterion was chosen to minimize the Hausdorff deviation of the arena from the union of these moving objects. Numerical algorithms are proposed for solving the problem, based on dividing the arena into areas of influence of the figures (into generalized Dirichlet zones) and finding the optimal position of each of them within the boundaries of its area. When creating the algorithms, non-smooth optimization methods and the constructions of the geometric theory of approximations were used. A numerical simulation of the solution of the problem is performed for the case of three moving convex polygons.