北京雁栖湖应用数学研究院

舟木 直久 , 吴劲松

Yaroslav Sergeev

2025年03月05日 17:00 至 18:00

A6-101

Zoom 388 528 9728 (BIMSA)

Global optimization is a thriving branch of applied mathematics and an extensive literature is dedicated to it (see [1-5] and references given therein). In this talk, we consider problems, methods, and applications in Lipschitz global optimization. It is supposed that the objective function satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant. The function to optimize can be `black box`, multiextremal, and non-differentiable. It is also assumed that evaluation of the objective function at a point is a time-consuming operation. Many algorithms for solving this problem have been discussed in the literature. They can be distinguished, for example, by the way of obtaining information about the Lipschitz constant and by the strategy of exploration of the search domain. Different exploration techniques based on various adaptive partition strategies are analyzed. A number of problems and applications related to Lipschitz global optimization are studied. Among them there are the search for the first zero-crossing point, safe global optimization, finding the working spaces of robots, etc. Issues related to the usage of numerical infinities and infinitesimals in global optimization (see [1]) are also discussed.
Selected references

1. Ya.D. Sergeyev and R. De Leone, eds. Numerical Infinities and Infinitesimals in Optimization. Springer, Cham, 2022.
2. Ya.D. Sergeyev, D.E. Kvasov, Deterministic Global Optimization: An Introduction to The Diagonal Approach, Springer, New York, 2017.
3. R. Paulavicius, J. Žilinskas, Simplicial Global Optimization. Springer, New York, 2014.
4. Ya.D. Sergeyev, R.G. Strongin, and D. Lera, Introduction to Global Optimization Exploiting Space-Filling Curves, Springer, New York, 2013.
5. R.G. Strongin and Ya.D. Sergeyev, Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms, Kluwer, Dordrecht, 2000.

Yaroslav D. Sergeyev is Distinguished Professor at the University of Calabria, Italy (chiamata diretta per chiara fama) and Head of Numerical Calculus Laboratory at the same university. Several decades he was also Affiliated Researcher at the Institute of High-Performance Computing and Networking of the Italian National Research Council, and is Affiliated Faculty at the Center for Applied Optimization, University of Florida, Gainesville, USA.
He was awarded his Ph.D. (1990) from Lobachevski Gorky State University and his D.Sc. degree (1996) from Lomonosov State University, Moscow (this degree is Habilitation for the Full Professorship in Russian universities). In 2013, he was awarded Degree of Honorary Doctor from Glushkov Institute of Cybernetics of The National Academy of Sciences of Ukraine, Kiev.
His research interests include global optimization (he was President of the International Society of Global Optimization, 2017-2021), infinity computing and calculus (the field he has founded), numerical computations, scientific computing, philosophy of computations, set theory, number theory, fractals, parallel computing, and interval analysis.