Plenary Lecture
Tropical Optimization: Some Problems, Methods, and Applications
Professor Nikolai Krivulin
Faculty of Mathematics and Mechanics
St. Petersburg State University
Russia
E-mail: nkk@math.spbu.ru
Abstract: We give an overview of multidimensional optimization problems formulated in terms of tropical (idempotent) mathematics, outline related solution methods, and discuss applications. We start with a motivating example and a brief introduction to tropical mathematics to provide an appropriate framework for further discussion. The optimization problems are defined as to minimize linear and nonlinear functionals on finite dimensional semimodules over idempotent semifields, subject to linear inequality and equality constraints. Furthermore, we show that some problems have complete closed-form solutions, whereas solutions for other problems are only known in the form of iterative computational schemes that find a particular solution if any, or indicate its absence. Finally, application examples of real-world problems are considered, which are drawn from project scheduling, location analysis, transportation networks, decision making, and discrete event systems.
Brief Biography of the Speaker: Nikolai Krivulin received a university degree in applied mathematics and operations research in 1983 from St. Petersburg State University, St. Petersburg, Russia. He got his Ph.D. degree in 1990 and D.Sc. degree in 2010 both in applied mathematics from the same university. He worked at the Computer Center of St. Petersburg State University from 1983 to 1985, when he stared his Ph.D. study. In 1987 he joined the Faculty of Mathematics and Mechanics at the University as an Assistant Professor, became there an Associate Professor in 1991 and a Professor in 2012. From 1999 to 2002 he was the head of the Department of Information Management at the Graduate School of Management of the same university.
He is currently a Professor of the Department of Statistical Modelling at St. Petersburg State University. His research interests include theory and applications of idempotent algebra, modelling and performance evaluation of queueing systems, methods of optimization, computational statistics and computer simulation. He is an author and coauthor of more than 80 publications including papers in reviewed journals and conference proceedings, books chapters, textbooks, and a monograph. He was a grantee of national and international foundations, including the Russian Foundation for Basic Research, the Russian Foundation for Humanities Research, the NATO Science Foundation, the USIA and Eurasia Foundation (USA), and the Royal Society (UK). He served as a member of program and organizing committees of international conferences on mathematics, computer sciences, and information technology. He is a member of the St. Petersburg Mathematical Society, AMS, and SIAM.