1. Speaker: Dr. Anton Bondarev, International Business School Suzhou, Xi'an Jiaotong-Liverpool University, P. R. China.
Title: Optimality of sliding dynamics in hybrid control systems
There is growing evidence on the presence of sliding dynamics in many piecewise-smooth dynamical systems (PWS), reported in papers on population biology, renewable resources and etc. However to our best knowledge there are no studies on the optimality of such a type of dynamics. This talk will go through some recent advances in the theory of hybrid optimal control which deals with PWS dynamics and present findings on the optimality of the sliding dynamics in such systems, both in the optimal control problems and differential games. Moreover some results on the presence of hybrid limit cycles in such systems will be discussed.
In particular, hybrid control problem may have the equilibrium of the sliding flow as the only possible long-run outcome if all conventional equilibria of the PWS at hand are infeasible. Moreover, this equilibrium may be reached only from the outside of the sliding flow itself. Next, hybrid limit cycles (HLC) may be optimal or not depending on the definition of the switching manifold and the dimensionality of the problem.
At last, some further open questions of interest in the field are discussed.
2. Speaker: Prof. Nenad Mladenovic, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates
Title: Formulation Space Search Metaheuristic
Many methods for solving discrete and continuous global optimization problems are based on changing one formulation to another, which is either equivalent or very close to it. These types of methods include dual, primal-dual, Lagrangian, linearization, surrogation, convexification methods, coordinate system change, discrete/continuous reformulations, to mention a few. However, in all those classes, the set of formulations of one problem are not considered as a set having some structure provided with some order relation among formulations. The main idea of Formulation Space Search (FSS) is to provide the set of formulations with some metric or quasi-metric relations, used for solving a given class or type of problem. In that way, the (quasi) distance between formulations is introduced, and the search space in solving Global optimization problems is extended to the set of formulations as well. In this talk I will present the general methodology of FSS, and give an overview of several applications taken from the literature that fall within this framework. I will also examine two of these applications in more detail.
This is joint work with J Brimberg, R Todosijevic and D Urosevic.
3. Speaker: Prof. Yurii Nesterov,CORE/INMA, Université Catholique de Louvain, Belgium
Title: Inexact high-order proximal-point methods with auxiliary search procedure
In this talk, we present new framework of Bi-Level Unconstrained Minimization based on high-order proximal-point method with the maximal convergence rate O(1/k^((1+3p)/2)), where k is the iteration counter and p is the order of the scheme. Under assumption on the boundedness of the (p+1)th derivative of the objective function, each iteration of the scheme can be implemented by one step of the pth order augmented tensor method. In this way, for p = 2, we get a new second-order method with the rate of convergence O(1/k^(7/2)) and logarithmic complexity of the auxiliary search at each iteration. Another possibility is to compute the proximal-point operator by a lower-order minimization method. As an example, for p = 3, we consider the upper-level process convergent as O(1/k^5). Assuming boundedness of the fourth derivative, an appropriate approximation of the proximal-point operator can be computed by a second-order method in a logarithmic number of iterations. This combination gives a second-order scheme with much better complexity than the existing theoretical limits.
4. Speaker: Prof. Panos M. Pardalos, University of Florida, USA
http://www.ise.ufl.edu/pardalos/ & https://nnov.hse.ru/en/latna/
Title: Artificial Intelligence, Data Sciences, and Optimization in Economics
Artificial Intelligence (along with data sciences and optimization)
has been a fundamental component of many activities in economics and
finance in recent years. In this lecture we first summarize some of
the major impacts of AI tools in economics and finance and discuss
future developments and limitations. In the second part of the talk we
present details on neural network embeddings on corporate annual
filings for portfolio selection.
5. Speaker: Prof. Alexey Tret'yakov, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Title: Exit from singularity. New optimization methods and the p-regularity theory applications
We introduce a new nonsingular operator instead of a degenerate operator of the first derivative in a singular case for solving and describing nonregular optimization problems and some problems in calculus. Such operator is called p-factor-operator and its construction is based on the derivatives up to order p as well as on some element h, which we call the "exit from singularity".
The special variant of the method of the modified Lagrange functions for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation and constructions of p-regularity theory. These results are used in some classical branches of calculus: implicit function theorem is given for the singular case and is shown the existence of solutions to a boundary-valued problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.
This is joint work with Yuri Evtushenko and Vlasta Malkova.