Bayesian and High-Dimensional Global Optimization

Beschreibung

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. 

Autor*in

Anatoly Zhigljavsky

Themen in »Bayesian and High-Dimensional Global Optimization«

Global optimization High-dimensional optimization Global random search Bayesian global optimization Expensive black-box functions P-algorithm Multidimensional spaces and sets matrix theory

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“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)
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