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
Jack Noonan is a postdoctoral researcher at Cardiff University School of Mathematics, UK. At Cardiff University, he received a PhD on applied probability and statistics in 2021 and received a BSc in Mathematics, Operational Research and Statistics in 2017. His areas of research include high-dimensional optimization and inference, change-point detection, group testing, modelling of epidemics and missing data. Anatoly Zhigljavsky is a professor of mathematics and statistics at Cardiff University, UK. He holds this post since 1997. He received PhD (and then habilitation) on applied probability and computational mathematics in 1981 (respectively, in 1986) at St. Petersburg State University. He is the author or co-author of 12 monographs on the topics of stochastic global optimization (five), time series analysis (four), optimal experimental design (two) and dynamical systems (one); editor/co-editor of 12 books or special issues of journals on the topics above, the author of more than 200 research papers in refereed journals, organizer of several major conferences on kernel methods in machine learning, time series analysis, experimental design, and global optimization. Professor Zhigljavsky is a recipient of a prestigious Constantine Caratheodory award (2019) by the International Society for Global Optimization for his life-time achievement in the field of stochastic global optimization.

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.