1. Speaker: Prof. Yurii Nesterov,CORE/INMA, Université Catholique de Louvain, Belgium

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

Title: Universality, the new trend in development of Optimization Schemes

Abstract:

In the early years of Optimization, the first classical schemes were derived from an abstract concept of approximation (e.g. Gradient method, Newton’s methods, etc.). However, since the development of Complexity Theory for Convex Optimization (Nemirovsky, Yudin 1970’s), the most powerful approaches for constructing efficient (optimal) methods are based on the model of the objective function. This model incorporates the characteristic properties of the corresponding problem class and provides us with a comprehensive information on the behavior of the objective. At the same time, it helps in deriving theoretically unimprovable complexity bounds for the target class.

However, this framework completely neglects the fact that every objective function belongs, at the same time, to many different problem classes. Hence, it should be treated by a method developed for the most appropriate class of problems. However, for the real-life problems, such a choice is seldomly feasible, at least in advance.

In this talk, we discuss several ideas for constructing universal methods, which automatically ensure the best possible convergence rate among appropriate problem classes. The simplest methods of this type adjust to the best power in Holder condition for the target derivative. Our most promising super-universal Regularized Newton’s Method works properly for a wide range of problems, starting from the functions with bounded variation of Hessian up to the functions with Lipschitz continuous third derivative. Thus, being a second-order scheme, it covers all diversity of problems, from the problems traditionally treated by the first-order methods, up to the problems, which are usually attributed to the third-order schemes. For its proper work, no preliminary information on the objective function is needed.

(Some of the results are obtained jointly with N. Doikov, G. Grapiglia, and K. Mishchenko.)

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

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

Short CV

Title: Diffusion in Networks

Abstract:

This lecture addresses the significant challenge of comprehending diffusive processes in networks in the context of complexity. Networks possess a diffusive potential that depends on their topological configuration, but diffusion also relies on the process and initial conditions. The lecture introduces the concept of Diffusion Capacity, a measure of a node’s potential to diffuse information that incorporates a distance distribution considering both geodesic and weighted shortest paths and the dynamic features of the diffusion process. This concept provides a comprehensive depiction of individual nodes’ roles during the diffusion process and can identify structural modifications that may improve diffusion mechanisms. The lecture also defines Diffusion Capacity for interconnected networks and introduces Relative Gain, a tool that compares a node’s performance in a single structure versus an interconnected one. To demonstrate the concept’s utility, we apply the methodology to a global climate network formed from surface air temperature data, revealing a significant shift in diffusion capacity around the year 2000. This suggests a decline in the planet’s diffusion capacity, which may contribute to the emergence of more frequent climatic events. Our goal is to gain a deeper understanding of the complexities of diffusive processes in networks and the potential applications of the Diffusion Capacity concept.

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

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

Title: The pth-order Karush-Kuhn-Tucker type optimality conditions for nonregular inequality constrained optimization problems

Abstract:

We present necessary and sufficient optimality conditions for optimization problems with inequality constraints in the finite dimensional spaces. We focus on the degenerate (nonregular) case when the classical constraint qualifications are not satisfied at a solution of the optimization problem.
We present optimality conditions of the Karush-Kuhn-Tucker type under new regularity assumptions. To formulate the optimality conditions, we use the p-factor operator, which is the main construction of the p-regularity theory. The approach of p-regularity used in the paper can be applied to various degenerate nonlinear optimization problems due to its flexibility and generality.

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