Prof. Y.D. Sergeyev
University of Calabria, Italy
Title: Numerical infinities and infinitesimals in optimization
Abstarct: In this talk, a recent computational methodology is described (see [1,2]). It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework. It is based on the principle ‘The part is less than the whole’ applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses as a computational device the Infinity Computer (a new kind of supercomputer patented in several countries) working numerically with infinite and infinitesimal numbers that can be written in a positional system with an infinite radix. On a number of examples (numerical differentiation, divergent series, ordinary differential equations, etc.) it is shown that the new approach can be useful from both theoretical and computational points of view. The main attention is dedicated to applications in optimization (local, global, and multi-objective, see [1,2-7]). The accuracy of the obtained results is continuously compared with results obtained by traditional tools used to work with mathematical objects involving infinity.
Bio: 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.