### Book

## Mathematical Optimization Theory and Operations Research, 18th International Conference, MOTOR 2019 Ekaterinburg, Russia, July 8–12, 2019

Let f:R^n→R be a conic function and x_0∈R^n. In this note, we show that the shallow separation oracle for the set K={x∈R^n:f(x)≤f(x_0)} can be polynomially reduced to the comparison oracle of the function *f*. Combining these results with known results of D. Dadush et al., we give an algorithm with (O(n))^n*logR calls to the comparison oracle for checking the non-emptiness of the set K∩Z^n, where *K* is included to the Euclidean ball of a radius *R*. Additionally, we give a randomized algorithm with the expected oracle complexity (O(n))^n*logR for the problem to find an integral vector that minimizes values of *f* on an Euclidean ball of a radius *R*. It is known that the classes of convex, strictly quasiconvex functions, and quasiconvex polynomials are included into the class of conic functions. Since any system of conic functions can be represented by a single conic function, the last facts give us an opportunity to check the feasibility of any system of convex, strictly quasiconvex functions, and quasiconvex polynomials by an algorithm with (O(n))^n*logR calls to the comparison oracle of the functions. It is also possible to solve a constraint minimization problem with the considered classes of functions by a randomized algorithm with (O(n))^n*logR expected oracle calls.Let f:R^n→R be a conic function and x_0∈R^n. In this note, we show that the shallow separation oracle for the set K={x∈R^n:f(x)≤f(x_0)} can be polynomially reduced to the comparison oracle of the function *f*. Combining these results with known results of D. Dadush et al., we give an algorithm with (O(n))^n*logR calls to the comparison oracle for checking the non-emptiness of the set K∩Z^n, where *K* is included to the Euclidean ball of a radius *R*. Additionally, we give a randomized algorithm with the expected oracle complexity (O(n))^n*logR for the problem to find an integral vector that minimizes values of *f* on an Euclidean ball of a radius *R*. It is known that the classes of convex, strictly quasiconvex functions, and quasiconvex polynomials are included into the class of conic functions. Since any system of conic functions can be represented by a single conic function, the last facts give us an opportunity to check the feasibility of any system of convex, strictly quasiconvex functions, and quasiconvex polynomials by an algorithm with (O(n))^n*logR calls to the comparison oracle of the functions. It is also possible to solve a constraint minimization problem with the considered classes of functions by a randomized algorithm with (O(n))^n*logR expected oracle calls.

Algorithmization of the quality of queueing systems is carried out in oder to optimize the work, constructing the revenue functional on the trajectories of a managed semi-Markov process while managing the system's structure. In particular, we consider both semi-Markov and Markoqueueing systems with control of several parameters chaaractirestics of the system). The task is to find the optimal management strategy.

This paper discusses the application of genetic algorithms for the scheduling of electric rolling stock maintenance. The main objective is to improve the automated train scheduling system of uniformity maintenance process with a variety of maintenance resources, including the limited resources. The methods of graph theory and Bellman principle allow us to get the entire set of suitable maintenance schedules and choose which maintenance corresponds to the train schedule, and the minimum differs from the optimal one according to the selected criteria. Traditionally, it takes a significant amount of time and the main problem is using the criterion of uniformity maintenance under limited resources. In this case, we used genetic algorithm for optimization. The results showed that the genetic algorithm is an effective tool for optimization of maintenance scheduling.

This chapter elaborates on entrepreneurship in developed and developing countries and focuses on the optimization of entrepreneurial activities. Various scenarios are considered: independent functioning of the market, integration in the form of reorganization (mergers and acquisitions), integration in the form of clustering, and integration in the form of innovational networks and technological parks. The optimal structure of the integration processes and best-case scenarios for its implementation to accelerate the rate and increase the quality of economic growth are substantiated. The potential for uptake of integration processes in stimulating economic growth through entrepreneurship is determined by the level of institutionalization in an economy. In developed countries, all forms of company integration are characterized by the high level of institutionalization, which allows for their effective use for economic growth. Independent companies, mergers, and acquisitions restrain economic growth and reduce its quality, while clusters, technological parks, and innovational networks accelerate the rate of economic growth and increase its quality. In developing countries, integration processes in entrepreneurship have a different influence on economic growth and require further institutionalization

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known *a priori*.

Book include abstracts of reports presented at the IX International Conference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2018) held in Petrovac, Montenegro, October 1 - October 5, 2018.

Distinguishing outliers from normal data in wireless sensor networks has been a big challenge in the anomaly detection domain, mostly due to the nature of the anomalies, such as software or hardware failures, reading errors or malicious attacks, just to name a few. In this article, we introduce an anomaly detection-based OPF classifier in the aforementioned context. The results are compared against one-class support vector machines and multivariate Gaussian distribution. Additionally, we also propose to employ meta-heuristic optimization techniques to finetune the OPF classifier in the context of anomaly detection in wireless sensor networks.

The task is to sharply reduce the complexity of analysis, multivariate analysis and parametric optimization of linear and linearized equivalent electrical circuits. The source of such schemes are not only linear electronic circuits, but also circuits formed on the basis of artificial electrical analogies. They can be formed on the basis of finite element methods and finite difference methods used in solving partial differential equations. The reduction in the complexity of computations is carried out by formal methods of transforming the model into a macromodel, which reflects only the input - output type relations of the original model. The e ssence of the work lies in the formal transformation of the model of a linear or linearized equivalent electrical circuit, formed using artificial electrical analogies methods, into a macromodel, according to which the same output characteristics can be calculated with the same accuracy but with increased speed by several orders of magnitude. Algorithms for such transformations are given. Using a macromodel, one can calculate static characteristics, frequency characteristics, zeros and poles of system functions, dynamic characteristics, eigenvalues, and vectors of a macromodel matrix, which make it possible to determine the stability and stability margin of the original circuit using the first А.М. Lyapunov method, its resonant eigenfrequencies and the duration of the transition process, as well as partial derivatives of the above characteristics for a small number of variable circuit parameters to replace the optimization of the circuit with the methods of the 1st order with its optimization by the macro model. In addition, macromodels can be used to create a new element, constructional, and technological base for design. Macromodel can serve as an element of a model of a higher hierarchical level. Block hierarchical process of macromodelling is possible.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.