This paper presents a comparison of three popular optimization methods: conjugate gradient method, Newton's method and DFP method. These methods are widely used to find the minimum of functions in various fields such as machine learning, robotics and engineering. The practical significance of the paper is to provide researchers and developers with tools to select the most appropriate optimization method for a particular problem, and to introduce the basics of optimization algorithms and their implementation in Matlab. The paper presents a point-by-point algorithm for each method, as well as the implementation of these algorithms in Matlab CAD. The results of the comparative analysis are illustrated with graphs and tables of values to evaluate the accuracy and convergence rate of each method. The materials of the paper, including program code and mathematical calculations, are available in the public domain, which allows anyone to repeat the experiments and verify the results obtained. This paper can be used by students of technical universities to solve problems of any complexity, to obtain an optimal solution, for example, when searching for the minimum of a function.
