The aim of this article is to show the possibilities of using mathematical programming models in classification problems using the committee machine method. Classification problems can be found in many practical problems, so the development of classification methods is an important area of research. At the same time, the application of mathematical programming is a little studied topic. The paper presents restrictions and objective functions for mathematical programming models within which various logics of committee constructions are implemented. A description quality metrics in classification models and their implementation in form of mathematical programming, as well as the graphical interpretations of the committee logics. The author's interpretation of the condition for reducing the dimension of the problem by choosing the most informative features within the framework of a unified model of mathematical programming is presented. The proposed method allows to achieve high classification quality, to minimize the number of features in classification problems and to provide a geometric interpretation of the solutions. The described models were tested by the authors in problems from such areas as: the healthcare, metallurgy, bank scoring and stock exchange market.