Plenary Lecture
Multidimensional Optimization Problems in Tropical Mathematics with Applications to Location Analysis
Associate Professor Nikolai Krivulin
Faculty of Mathematics and Mechanics
St. Petersburg State University
RUSSIA
E-mail: nkk@math.spbu.ru
Abstract: We consider multidimensional optimization problems that are formulated in the tropical (idempotent) algebra setting. The problems under study are to minimize nonlinear functionals defined on finite-dimensional semimodules over idempotent semifields, and they may have additional constraints imposed on the feasible solution set in the form of linear equations and inequalities. We start with a brief introduction into idempotent algebra, and then overview preliminary results including solutions to linear equations and eigenvalue-eigenvector problems to provide a framework for further results. Furthermore, we examine unconstrained problems and give general comprehensive solutions to the problems in a closed-form. These solutions are then extended to handle certain constrained problems. Finally, the above results are applied to both unconstrained and constrained multidimensional minimax single facility location problems with Chebyshev and rectilinear distances.
Brief Biography of the Speaker: Nikolai Krivulin received a university degree in applied mathematics and operations research in 1983 from St. Petersburg State University (SPbSU). He got his Ph.D. degree in 1990 and D.Sc. degree in 2010 both in applied mathematics from SPbSU. In 1983 he joined the Computer Center at SPbSU as a system software engineer, and in 1985 started his Ph.D. study. In 1987 he joined the Faculty of Mathematics and Mechanics at SPbSU as an Assistant Professor, and became an Associate Professor in 1990. From 1999 to 2002 he was the head of the Department of Information Management in the Graduate School of Management at SPbSU.
He is currently an Associate 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 author and coauthor of more than 70 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.