The implementation of the “Digital transformation in the Russian Federation” program is a national goal, a powerful conglomerate for the development of the Russian economy and is aimed at understanding, formulating and implementing strategies and tactics for the development of education, business and society as a whole. In the situation of a high degree of uncertainty caused by external environment and internal problems, universities today, more than ever before, cannot fail to fill in the gaps between the needs of the labor market and the professional competencies formed in the university for it. The university has all the opportunities to increase the human capital of the region, which is defined as the structure of knowledge, skills, and intellectual potential with the ability to apply them in work to create added value and is formed, among other things, by the university education system. The article presents a look at the content of the multicomponent electronic educational environment of the Master’s training in the field of Applied Informatics, which is built on the principles of consistency, which takes into account all aspects of the modern educational process: personnel, technology, educational resources.

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods in solving single scalar equations. Our strategy is to control the speed of the convergence of gradient methods through the step size value defined using more parameters. As a result, efficient minimization schemes for solving SNE are introduced. Linear global convergence of the proposed iterative method is confirmed by theoretical analysis under standard assumptions. Numerical experiments confirm the significant computational efficiency of proposed methods compared to traditional gradient descent methods for solving SNE.

The aim of this study is to solve the problem of increasing the efficiency of fuel and energy complex enterprises. Because such enterprises are complex systems, it is difficult to optimize their work, taking into account all the technical indicators of such enterprises. This study proposes to solve this problem by defining an algorithm using the data envelopment analysis (DEA) method. In particular, the algorithm was applied in heating systems using the example of a combined heat and power plant, where the DEA method had not previously been used. Experiments were carried out to improve the efficiency of the combined heat and power plant. Efficiency indicators were calculated, changing inputs and outputs of the model according to the study case to achieve the maximum efficiency of the system. The Charnes; Cooper and Rhodes; and the Banker, Charnes, and Cooper models were tested with good results. The presented methodology and experimental results enabled the DEA method to be applied for the first time to improve the efficiency of fuel and energy companies.

The article substantiates the need to adjust corporate development strategies, business models and production methods, caused by the influence of the fourth industrial revolution (Industry 4.0). Cluster and network structures are capable of ensuring timely digital business transformation. For effective integration into network interaction, it is necessary to form corporate strategies for innovative development based on an effective combination of strategic and operational planning using network methods. The article provides a comparative analysis of the critical path method, the method of evaluation and analysis of programs and projects, the method of graphical assessment and analysis, and the cyclical alternative network model. As a result of the study of network planning methods, it was revealed that the GERT-network modelling allows taking into account the risk factors and uncertainties, and the cyclical alternative network model allows to manage the level of risk and uncertainty. The two-level model of planning and management of industrial production proposed in the article, as well as the developed algorithm for solving the problem of interdepartmental production planning, can be used as the basis for the formation of a strategy for the innovative development of industrial enterprises.

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability.