The paper investigates a multi-stage investment problem under Conditional Value at Risk (CVaR) constraints with: a given security level for bankruptcy, short selling permission, a normal and an elliptical total return distribution models. The purpose of the work is to find a method of determining the optimal investment in this problem at each stage. As a result of the study, an optimal investment strategy is found and it is shown that the optimal investment portfolio at each stage does not depend on the value of the investor’s capital, but depends only on the number of stage. It is shown that the multi-stage problem can be reduced to a finite number of one-stage optimization problems, which are problems of conic programming. For the one-stage problem, conditions for the non-emptiness of the set of admissible portfolios are given and the Kuhn–Tucker theorem is applied. Additionally, this paper presents a numerical example of finding the optimal investment based on the open data on rates of assert prices of companies on the stock exchange.

The prerequisites for the emergence of the theory of hierarchical games are described. The models are described and linked to a set of articles that give an idea of the key problems and the fundamental results obtained. Attention is paid to practical applications. The basic concepts and provisions are illustrated by solutions in the case of linear problems. In conclusion, the need for further research in the field of computational methods is noted.

In this work, we explore the challenges associated with the formation of satellite measurement datasets for constructing models of Mars’ magnetic field. Several approaches to dataset construction have been proposed and implemented. Using the regional method of S-approximations, analytical approximations of the magnetic field have been developed, and analytical continuations of the field to a uniform selected altitude have been presented. Calculations were performed for an area of Mars that includes the landing sites of the InSight spacecraft and the Chinese rover Zhurong. The modeling was based on datasets derived from calibrated insitu.calibrated level 2 data of the MAVEN mission.

This paper considers an oligopoly model with an arbitrary number of Cournotreflexive agents under incomplete information in the classical case of linear cost and demand functions. Agents make decisions based on a collective behavior model. The problem of identifying convergence conditions to the model equilibrium is studied, with an emphasis placed on the trajectory of the sum of the action residuals of all agents. Aggregate estimates of this trajectory are obtained. They can be used to judge how the trajectory of each agent evolves towards the equilibrium.

The paper considers a state observer-based iterative learning control design problem for discrete linear systems. To accelerate the convergence of the learning error, a combination of the heavy ball method from optimization theory and the vector Lyapunov function method for a class of two-dimensional systems known as repetitive processes is used to develop a new design. A supporting numerical example is given, including a comparison with an existing design.

The time-optimal control problem for an arbitrary number of nonsynchronous oscillators with a limited scalar control is considered. An analytical investigation of the problem is performed. The property of strong accessibility and global controllability is proved, and a program control is found that brings the system from the origin to a fixed point in the shortest time. Trajectories satisfying both the motion equations of the system and the additional conditions based on the matrix nondegeneracy conditions of the relay control have been found for bringing a group of oscillators to the origin. Two classification methods of trajectories according to the number of control switchings are compared: the one based on the necessary extremum conditions and the Neustadt–Eaton numerical algorithm.

Digital twins reflect the state of the environment and the activities of enterprises affected by the hydrometeorological conditions. It is proposed to use models to calculate indicators for assessing impacts of natural hazards or of climate change; of forecasts of these impacts; damage estimates; of calculating the cost of actions to protect enterprises; of assessing the feasibility of carrying out preventive actions in order to optimize them. Requirements for impact assessment models working with a digital twin are given. The difficulties in using such models are presented. Proposals for the development of impact models are being considered. A diagram of the use of digital twins in modeling impacts of environmental on enterprises is shown.

This paper reports of theoretical and computational results related to an original concept of consensus clustering involving what we call the projective distance between partitions. This distance is defined as the squared difference between a partition incidence matrix and its image over the orthogonal projection in the linear space spanning the other partition incidence matrix. It appears, provided that the ensemble clustering is of a sufficient size, agglomerate clustering with the semi-average within-cluster similarity criterion effectively solves the problem of consensus partition and, moreover, of the number of clusters in it.