Тема доклада будет объявлена позднее.

The transition towards sustainable cities becomes an increasingly pressing issue because of the growing awareness about the climate change. One of the critical transition directions is to reduce the greenhouse gas emissions generated by transportation. One of efficient answers to this challenge is the implementation of electric public transportation systems. In order to achieve the best impact, it is imperative to design the infrastructure and the network of the public transportation in an optimized way. The following problems concerning strategic, tactical and operational aspects of the electric bus planning process and scheduling are discussed: a) investment of electric bus fleet and charging infrastructure; b) design of charging infrastructure; c) the electric vehicle scheduling; d) the charging scheduling problem. The models and optimization methods for different charging technologies are considered:
- slow plug-in chargers installed at bus depots;
- fast plug-in or pantograph chargers installed at terminals of bus lines or at bus stops;
- overhead contact lines or inductive (wireless) chargers that are used to recharge buses during driving;
- battery swapping.

In the last decade the usage of optimization methods for performance estimation and tuning of other optimization methods has became fashionable. For instance, semi-definite programming allows to analyze the behaviour of accelerated gradient descent methods at minimizing functions of different regularity. Detecting the worst-case performance with respect to the minimized function and maximizing this performance with respect to the parameters of the method allows to obtain the best parameter set.
Here we show how to perform a similar analysis of the Newton method when minimizing self-concordant functions. This task arises as a subproblem in more complex structured convex optimization problems such as semi-definite programming inside path-following methods. The appropriate framework for optimizing the parameters, in particular, the step length and the search direction, is optimal control theory. We present a general technique to use the Pontryagin maximum principle in the analysis of the Newton step on a self-concordant function and specialize it in several case studies.
The talk in part presents joint work with Anastasia Ivanova.

In this talk, some recent results in domination theory are presented. In 2020, T.W. Haynes et al. introduced coalitions and coalition partitions based on dominating sets in graphs as a graph-theoretical model to describe political coalitions. The authors have been studied the property of this concept and suggested a list of open problems. In particular, it was suggested to study connected coalitions based on connected dominating sets. In this talk we focus on studying connected coalitions and their partitions in graphs with emphasising to polynomial-time algorithms determining whether the connected coalition number of a graph G of order n is either n or n-1. The talk is based on joint works with S. Alikhani, D. Bakhshesh, and H. Golmohammadi.

Panos M. Pardalos, University of Florida
www.ie.ufl.edu/pardalos
https://nnov.hse.ru/en/latna/

Advances in AI tools are progressing rapidly and demonstrating the potential to transform our lives. The spectacular AI tools rely in part on their sophisticated mathematical underpinnings (e.g. optimization techniques and operations research tools), even though this crucial aspect is often downplayed.

In this lecture, we will discuss progress from our perspective in the field of AI and its applications in Energy systems and Sustainability.

In this talk we present the mathematical description of the economic behavior of a rational household in consumer loan market. The modeling of the economic behavior of households is based on the concept of a rational representative economic agent and arises to F. Ramsey. The model is formalized as an optimal control problem on a finite time horizon. The household maximizes discounted consumption with constant risk aversion, managing the dynamics of its expenditures depending on the current parameters of the economic situation and the behavioral characteristics of the household itself. We consider an imperfect market when the interest rate on loans differs from the interest rate on deposits. The difference in interest rates on loans and deposits leads to non-smoothness of the right-hand side of the differential equation for the phase variable. This motivates to use the Pontryagin maximum principle in the form of F. Clark. Applying it, we obtain an area where the household does not interact with the banking system, the special regimes arise. If we tend the time horizon of an optimal control problem to infinity, it is possible to construct a synthesis. The synthesis allows us to determine an optimal control depending on the current value of the phase variable and the parameters of the economic situation. It depends on current interest rates and on the behavioral characteristics of a representative household. We develop and investigate a new model for the formation of interest rates on consumer loans based on an analysis of commercial interests and the logic of behavior of commercial banks. The model assumes that the borrowers’ incomes are described by a geometric Brownian motion. The commercial banks assess the default risk of borrowers. According to the Feynman–Kac formula, the assessment is reduced to solving a boundary value problem for partial differential equations. An analytical solution to this problem is constructed. It is possible to reduce the solution of the boundary value problem to the Cauchy problem for the heat equation with an external source and obtain a risk assessment in analytical form with a help of the Abel equation. The models of economic behavior of households in the consumer loan market and behavior of commercial banks are identified based on Russian statistics. A specialized software has been developed to analyze the demand for consumer credit. With its help, the problems of the consumer lending market in Russia are analyzed.

Abstract: The recent revolutionary progress of artificial intelligence has brought significant challenges and opportunities to mathematical optimization. In this talk, we briefly discuss two examples on the integration of data, models, and algorithms for the development of optimization algorithms: ODE-based learning to optimize and learning-based optimization paradigms for solving integer programming. We will also report a few interesting perspectives on formalization and automated theorem proving, highlighting their potential impact and relevance in contemporary mathematical optimization.

Bio: Wen Zaiwen, Professor at Peking University. He mainly studies optimization algorithms and theory and their applications in machine learning. He was awarded the China Youth Science and Technology Award in 2016 and Beijing Outstanding Youth Zhongguancun Award in 2020. He was funded by the National Ten Thousand Talents Program for Science and Technology Innovation. He is an associate editor of “Journal of Scientific Computing”, "Communications in Mathematics and Statistics", "Journal of the Operations Research Society of China", "Journal of Computational Mathematics" and a technical editor of "Mathematical Programming Computation".

Distributed optimization is solved by the mutual collaboration among a group of agents, which arises in various domains such as machine learning, resource allocation, location in sensor networks and so on. In this talk, we introduce two kinds of distributed optimization problems: (i) the agents share a common decision variable and local constraints; (ii) the agents have their individual decision variables but that are coupled by global constraints.

This talk comprehensively introduce the origin of distributed optimization, classical works as well as recent advances. In addition, based on reinforcement learning, shortest path planning, and mixed integer programming, we build the distributed optimization framework of distributed optimization, and also discuss their applications. Finally, we make a summary with future works for distributed optimization.

В презентации представлены Элементы Теории Глобального поиска (ТГП) для задач оптимизации с целевой функцией и ограничениями типа равенства и неравенства, заданных DC функциями (разностями выпуклых функций). В таких задачах современный аппарат выпуклой оптимизации оказывается неоперабельным не только в смысле характеризации и отыскания глобального решения, но и при попытке «выскочить» из локального экстремума.

В докладе представлены основные свойства линейного пространства DC функций, в частности, что на компакте , и поэтому любая задача оптимизации с непрерывными данными может быть аппроксимирована, с любой заданной точностью, некоторой задачей DC оптимизации. Вначале основное внимание уделено каноническим задачам DC оптимизации, таким как выпуклые максимизация и DC минимизации на стандартных множествах, где представлен аппарат Условий Глобальной Оптимальности (УГО), составляющих ядро ТГП.

В центре рассмотрения находится задача DC оптимизации с DC ограничениями типа равенств и неравенств. С помощью Теории Точного Штрафа эта задача сводится к задаче без ограничений, целевая функция которой оказывается DC. Для последней задачи доказаны соответствующие УГО, инициирующие построение некоторой Схемы Глобального Поиска (СГП), использующей специальные Методы Локального Поиска (МЛокП), «внутри» которых применяются современные (классические) методы выпуклой оптимизации.

В заключение, представлены приложения разработанного подхода, такие как, численный поиск равновесий Нэша в биматричной игре, двухуровневая оптимизация, и классическая задача решения системы нелинейных уравнений (СНАУ). Приводится (ограниченный) список публикаций по математической оптимизации и оптимальному управлению.

Parallel computing on graphic processors (GPUs) is getting more and more popular. Since NVIDIA released the CUDA development tool, it has become convenient to use GPUs for general-purpose computing and not just for graphics display tasks. A feature of a GPU is the presence of a large (hundreds and thousands) number of cores, which allows to significantly speed up the calculation, but requires to design special parallel algorithms. While the development of traditional processors (CPUs) has recently slowed down, the characteristics of the GPU (number of cores, memory size, power consumption, and cost) are improving rapidly. In this tutorial, we will learn the basics of GPU computing in CUDA and OpenCL and briefly review the pros and cons of using GPUs in various discrete optimization algorithms.