  In the article we have obtained some estimates of the rate of convergence for
the recently proposed by Yu.E. Nesterov method of minimization of a convex
Lipschitz-continuous function of two variables on a square with a fixed side.
The method consists in solving auxiliary problems of one-dimensional
minimization along the separating segments and does not imply the calculation
of the exact value of the gradient of the objective functional. Experiments
have shown that the method under consideration can achieve the desired accuracy
of solving the problem in less time than the other methods (gradient descent
and ellipsoid method) considered, both in the case of a known exact solution
and using estimates of the convergence rate of the methods.
