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Stream: Plenary

Chair: Julius Žilinskas

1. Lipschitz global optimization
   Yaroslav Sergeyev
   
   
   

   Global continuous optimization is a thriving branch of applied mathematics. In this lecture, the global optimization problem of a multidimensional function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. It is supposed that the objective function 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.

   Several adaptive partition methods and strategies for estimating the Lipschitz constant are analyzed. The main attention is dedicated to two types of algorithms. The first of them is based on using space-filling curves in global optimization. A family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem is discussed. A number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search, etc. are presented. Diagonal global optimization algorithms is the second type of methods under consideration. They have a number of attractive theoretical properties and have proved to be efficient in solving applied problem

   References [1] R. G. Strongin and Ya. D. Sergeyev, Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms, Kluwer, Dordrecht, 2000. [2] Ya. D. Sergeyev and D. E. Kvasov, Diagonal Global Optimization Methods, FizMatLit, Moscow, 2008. In Russian. [3] Ya. D. Sergeyev, R. G. Strongin, and D. Lera, Introduction to Global Optimization Exploiting Space-Filling Curves, Springer, New York, 2013.

   Short biography Yaroslav D. Sergeyev is Distinguished Professor at the University of Calabria, Italy (professorship awarded by the Italian Government) and Head of Numerical Calculus Laboratory at the same university. He is also Member of the University International Council and Professor (part-time contract) at Lobachevsky Nizhniy Novgorod State University, Russia, Affiliated Researcher at the Institute of High Performance Computing and Networking of the Italian National Research Council, and Affiliated Faculty at the Center for Applied Optimization, University of Florida, Gainesville, USA. He was awarded his Ph.D. (1990) from Lobachevsky Nizhniy Novgorod 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 numerical analysis, global optimization (since 2016 he is Vice-President of the International Society of Global Optimization), infinity computing and calculus, philosophy of computations, set theory, number theory, fractals, parallel computing, and interval analysis. Prof. Sergeyev was awarded several research prizes (Pythagoras International Prize in Mathematics, Italy, 2010; 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.). His list of publications contains more than 200 items (among them 5 books). He is a member of editorial boards of 5 international journals and co-editor of 6 special issues. He delivered more than 50 plenary and keynote lectures at prestigious international congresses. He was Chairman of 4 international conferences and a member of Scientific Committees of more than 60 international congresses. He is Coordinator of numerous national and international research and educational projects. Software developed under his supervision is used in more than 40 countries of the world. Numerous magazines, newspapers, TV and radio channels have dedicated a lot of space to his research.