1. Speaker: Prof. Anatoly Antipin, Lomonosov Moscow State University, Russia

https://www.webofscience.com/wos/author/record/I-4593-2013

Title: Solving optimal control problems with guaranteed results

Abstract:

The optimal control problem with phase constraints and a boundary value problem at the right end is considered. Optimal control problems play a huge role in mathematical modeling, where the theory of creating guaranteed (mathematically justified) solutions is of particular importance. One of the main tools is the maximum principle, on the basis of which attempts have been made for almost 70 years to construct a theory for calculating guaranteed solutions to classes of problems (linear, quadratic, convex, smooth). During this time, mountains of calculations have been carried out to solve practical problems, many approaches have been created, but the results obtained are not always justified. The reason is that the maximum principle is only a necessary condition for optimality, so the results obtained with its help are subject to verification, whether they are really the desired solution. But the formulation of the principle includes dual variables. This can be interpreted as a hint to consider the problem in a wider space - on the Cartesian product of the spaces of primal and dual variables. In this case, the Lagrange function naturally arises, the saddle point of which, according to the Kuhn-Tucker theorem, is formed by solutions of mutually dual problems. A gradient field of rotation with the center at the saddle point arises, which requires the use of gradient methods of the saddle point type. In this paper, a method of this type is proposed and its convergence to the solution of the problem is proven for all components: strong - for phase, conjugate and terminal variables, weak - for controls.

Key words: optimal control, phase constraints, boundary value problems, linear programming, Lagrangian, solution methods, convergence, stability.

This is joint work with Elena Khoroshilova.

2. Speaker: Prof. Yurii Nesterov, Corvinus University, Hungary; Professor emeritus of UCLouvain, Belgium

https://uclouvain.be/fr/repertoires/yurii.nesterov

Title: High-Order Reduced-Gradient Methods for Composite Variational Inequalities

Abstract:

In this talk, we present a unified approach for constructing efficient methods for solving Variational Inequalities, presented in a composite form (CVI). This class of problems is close to the maximal one, which can be efficiently treated by numerical methods. At the same time, it is more difficult than the class of Convex Optimization Problems. All efficient methods for VI use an additional “extra-gradient” step. We propose a new interpretation of this step as a cutting plane for the optimal solution, reflecting the interaction of the monotone operator with the boundary of the feasible set. Contrary to the existing approaches, we introduce a universal extragradient step, which does not depend on the particular class of CVI. Consequently, our framework can be used for developing optimal methods for CVI, which are based on high-order oracles. 

3. Speaker: Prof. Panos M. Pardalos, University of Florida, USA

http://www.ise.ufl.edu/pardalos/ & https://toxeus.org

Short CV

Title: Introduction to data analytics for networks – a historical perspective and major advances

Abstract:

Data analytics for networks involves the use of advanced techniques and tools to extract insights and knowledge from large and complex datasets generated by network devices, applications, and services. This process involves collecting, storing, processing, and analyzing large amounts of data to identify patterns, trends, and anomalies that can provide valuable information for network operators. By leveraging data analytics, network researchers can make informed decisions about network planning, capacity management, service delivery, and customer experience. Additionally, data analytics can help network operators to detect and respond to security threats and attacks, by analyzing network traffic, identifying abnormal behavior, and detecting potential vulnerabilities. Overall, data analytics is a critical component of massive networks, enabling network researchers to extract valuable insights from massive datasets and improve network performance, efficiency, and security.

4. Speaker: Prof. Alexey Tret'yakov, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

https://www.researchgate.net/profile/Alexey_Tretyakov

Title: Singular optimization problems and P-factor apparatus for their analysis and solution

Abstract:

The paper is devoted to the optimization problems with equality constraints in the case when the Lagrange multiplier associated with the objective function might be equal to zero. We introduce a new modified Lagrange system which has a singular solution of the original optimization problem as its regular solution. We obtain conditions under which this solution is a regular locally unique solution of the modified Lagrange system. Our results are based on constructions of the p-regularity theory and the structure of the p-factor.

This is joint work with Olga Brezhneva, Yuri Evtushenko, and Vlasta Malkova.