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

## TL;DR

This paper analyzes a Nesterov-based method for minimizing convex Lipschitz functions of two variables on a fixed square, providing convergence estimates and demonstrating faster performance than traditional methods in experiments.

## Contribution

It introduces convergence estimates for Nesterov's method applied to a specific 2D convex minimization problem and compares its efficiency to gradient descent and ellipsoid methods.

## Key findings

- The method achieves desired accuracy faster than gradient descent.
- It outperforms the ellipsoid method in experiments.
- Convergence rate estimates are provided for the proposed approach.

## 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.