Overview
- Includes examples of the convergence in probability of random search
- Examines high-dimensional global optimization problems
- Discusses methodological issues in global optimization
Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)
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Table of contents (3 chapters)
Keywords
About this book
Accessible to a variety of readers, this book is of interest to specialists, graduate students and researchers in mathematics, optimization, computer science, operations research, management science, engineering and other applied areas interested in solving optimization problems. Basic principles, potential and boundaries of applicability of stochastic global optimization techniques are examined in this book. A variety of issues that face specialists in global optimization are explored, such as multidimensional spaces which are frequently ignored by researchers. The importance of precise interpretation of the mathematical results in assessments of optimization methods is demonstrated through examples of convergence in probability of random search. Methodological issues concerning construction and applicability of stochastic global optimization methods are discussed, including the one-step optimal average improvement method based on a statistical model of the objective function. A significant portion of this book is devoted to an analysis of high-dimensional global optimization problems and the so-called ‘curse of dimensionality’. An examination of the three different classes of high-dimensional optimization problems, the geometry of high-dimensional balls and cubes, very slow convergence of global random search algorithms in large-dimensional problems , and poor uniformity of the uniformly distributed sequences of points are included in this book.
Reviews
“The book is well written, the presentation is clear and easy to follow. Numerous pictures enrich the content and make it easier to understand. I recommend this book to the researchers in the area of global optimization – it may serve as a nice survey on the recent results about the randomized methods in GO. I also think that it would be very useful for graduate students … as well as for the practitioners focused on the methodology.” (Marcin Anholcer, zbMATH 1473.90134, 2021)
Authors and Affiliations
About the authors
Anatoly Zhigljavsky has received his BSc, MSc and PhD degrees in mathematics and statistics at Faculty of Mathematics, St.Petersburg State University. He became professor of statistics at the St.Petersburg State University in 1989. Since 1997 he is a professor, Chair in Statistics at Cardiff University. Anatoly Zhigljavsky is the author or co-author of 11 monographs on the topics of time series analysis, stochastic global optimization, optimal experimental design and dynamical systems; he is the editor/co-editor of 9 books on various topics and the author of more than 150 research papers in refereed journals. He has organized several major conferences on time series analysis, experimental design and global optimization. In 2019, he has received a prestigious Constantine Caratheodory award by the International Society for Global Optimization for his contribution to stochastic optimization.
Antanas Žilinskas is member of Lithuanian Academy of Sciences and professor of informatics at the Institute of Data Science and Digital Technologies of Vilnius university. His research interests include global and multi-objective optimization, visualization of multidimensional data, and optimal engineering design. He is author or co-author of several well-known monographs in optimization. His scientific achievements in global optimization are marked by the Caratheodory prize of the International Society of Global Optimization (2017). Prof. Žilinskas is a member of editorial boards of numerous international scientific journals. He also paid a lot of attention to teaching students and organizing studies of informatics, has prepared several textbooks on optimization and informatics.Bibliographic Information
Book Title: Bayesian and High-Dimensional Global Optimization
Authors: Anatoly Zhigljavsky, Antanas Žilinskas
Series Title: SpringerBriefs in Optimization
DOI: https://doi.org/10.1007/978-3-030-64712-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2021
Softcover ISBN: 978-3-030-64711-7Published: 03 March 2021
eBook ISBN: 978-3-030-64712-4Published: 02 March 2021
Series ISSN: 2190-8354
Series E-ISSN: 2191-575X
Edition Number: 1
Number of Pages: VIII, 118
Number of Illustrations: 16 b/w illustrations, 38 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Industrial and Production Engineering, Probability Theory and Stochastic Processes, Linear and Multilinear Algebras, Matrix Theory