北航数学论坛学术报告

Problems, methods, and applications in Lipschitz global optimization

Yaroslav D. Sergeyev

时间：2025年3月6日（周四）下午4:00-5:00

地点：沙河国实E404

摘要: 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.

R.G. Strongin and Ya.D. Sergeyev, Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms, Kluwer, Dordrecht, 2000.

报告人简介:

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.

He was awarded several research prizes (International Constantin Carathéodory Prize, International ICNAAM Research Excellence Award, International Prize of the city of Gioacchino da Fiore, all in 2023; Khwarizmi International Award, 2017; Pythagoras International Prize in Mathematics, 2010; EUROPT Fellow, 2016; Outstanding Achievement Award from the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, USA; Honorary Fellowship, the highest distinction of the European Society of Computational Methods in Sciences, Engineering and Technology, 2015; The 2015 Journal of Global Optimization (Springer) Best Paper Award; Lagrange Lecture, Turin University, Italy, 2010; MAIK Prize for the best scientific monograph published in Russian, Moscow, 2008, etc.). In 2020, he was elected corresponding member of Accademia Peloritana dei Pericolanti in Messina, Italy. Since 2020 he is included in the rating “Top 2% highly cited authors in Scopus” produced by Stanford University, the list “Top Italian Scientists. Mathematics”, the list of top researchers produced by Research.com, etc. In 2022, his biography has been published in Chinese by the journal Mathematical Culture. In 2023, the book “Primi Passi nell’Aritmetica dell’Infinito” authored by Prof. Davide Rizza from the University of East Anglia has been published. The book is dedicated to teaching the Infinity Computing methodology developed by Prof. Sergeyev.

His list of publications contains more than 300 items (among them 6 authored and 11 edited books and more than 130 articles in international journals). He is a member of editorial boards of one book series (Springer), 12 international and 3 national journals and co-editor of 14 special issues. He delivered more than 90 plenary and keynote lectures and tutorials at prestigious international congresses. He was Chairman of 7 and Co-Chairman of 8 international conferences and a member of Scientific Committees of more than 110 international congresses. He is Coordinator of numerous national and international research and educational projects, supervises master and Ph.D. theses, takes part of Ph.D. commissions in Italy and abroad. Numerous magazines, newspapers, TV and radio channels have dedicated a lot of space to his research. In 2023, the 21st International Conference of Numerical Analysis and Applied Mathematics, Crete (Greece) has been dedicated to the achievements of Prof. Sergeyev and his 60th birthday.

邀请人：夏勇

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