One Method for Minimization a Convex Lipschitz-Continuous Function of 2 Variables on a Fixed Square

Abstract

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.