  The goal of the paper is development of an optimization method with the
superlinear convergence rate for a nonsmooth convex function. For optimization
an approximation is used that is similar to the Steklov integral averaging. The
difference is that averaging is performed over a variable-dependent set, that
is called a set-valued mapping (SVM) satisfying simple conditions. Novelty
approach is that with such an approximation we obtain twice continuously
differentiable convex functions, for optimizations of which are applied methods
of the second order. The estimation of the convergence rate of the method is
given.
