Bayesian and High-Dimensional Global Optimization

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.

Includes examples of the convergence in probability of random search Examines high-dimensional global optimization problems Discusses methodological issues in global optimization

Autorentext
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 ilinskas 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. ilinskas 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.

Zusammenfassung
"The book is well and intelligibly written. The text is accompanied by a lot of nice pictures, each chapter concludes with a list of references. The book is intended for a wide range of readers interested in the theoretical aspects of global optimization, methodology or applications of global optimization." (Ctirad Matonoha, Mathematical Reviews, April, 2022)
"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)

Inhalt

1 Space-lling in high-dimensional sets.- 2 Bi-objective decisions and partition based methods in Bayesian global optimization.- 3 Global random search in high dimensions.

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