Mirror version of similar triangles method for constrained optimization problems

Science about optimization methods is rapidly developing today. In machine learning, computer vision, biology, medicine, construction and in many other different areas optimization methods have vast popularity and they appear as important tool. One of the most important goals in optimization: create some "universal" method, which will have good performance in all problems regardless smoothness of a task, computation precision of gradient and other parameters which characterize a problem. In this thesis we propose a method which is "universal" for different problems and, at the same time, is simple for understanding.