04308nam a22005415i 4500 978-3-031-58909-6 DE-He213 20251030112248.0 cr nn 008mamaa 240601s2024 sz | s |||| 0|eng d 9783031589096 978-3-031-58909-6 10.1007/978-3-031-58909-6 doi QA402.5-402.6 PBU bicssc MAT042000 bisacsh PBU thema Noonan, Jack. author. aut http://id.loc.gov/vocabulary/relators/aut 78021 High-Dimensional Optimization [electronic resource] : Set Exploration in the Non-Asymptotic Regime / by Jack Noonan, Anatoly Zhigljavsky. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 143 p. 161 illus., 159 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs in Optimization, 2191-575X Introduction -- Chapter 1 High-dimensional cubes, balls and spherically symmetric distributions -- Chapter 2 Space exploration: partial covering and quantization. This book is interdisciplinary and unites several areas of applied probability, statistics, and computational mathematics including computer experiments, optimal experimental design, and global optimization. The bulk of the book is based on several recent papers by the authors but also contains new results. Considering applications, this brief highlights multistart and other methods of global optimizations requiring efficient exploration of the domain of optimization. This book is accessible to a wide range of readers; the prerequisites for reading the book are rather low, and many numerical examples are provided that pictorially illustrate the main ideas, methods, and conclusions. The main purpose of this book is the construction of efficient exploration strategies of high-dimensional sets. In high dimensions, the asymptotic arguments could be practically misleading and hence the emphasis on the non-asymptotic regime. An important link with global optimization stems from the observation that approximate covering is one of the key concepts associated with multistart and other key random search algorithms. In addition to global optimization, important applications of the results are computer experiments and machine learning. It is demonstrated that the asymptotically optimal space-filling designs, such as pure random sampling or low-discrepancy point nets, could be rather inefficient in the non-asymptotic regime and the authors suggest ways of increasing the efficiency of such designs. The range of techniques ranges from experimental design, Monte Carlo, and asymptotic expansions in the central limit theorem to multivariate geometry, theory of lattices, and numerical integration. This book could be useful to a wide circle of readers, especially those specializing in global optimization, numerical analysis, computer experiments, and computational mathematics. As specific recipes for improving set exploration schemes are formulated, the book can also be used by the practitioners interested in applications only. . Mathematical optimization. 65522 Stochastic processes. 76770 Mathematics Data processing. 65715 Optimization. 65528 Stochastic Processes. 76770 Computational Mathematics and Numerical Analysis. 66073 Zhigljavsky, Anatoly. author. aut http://id.loc.gov/vocabulary/relators/aut 78022 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031589089 Printed edition: 9783031589102 SpringerBriefs in Optimization, 2191-575X 78023 https://doi.org/10.1007/978-3-031-58909-6 ZDB-2-SMA ZDB-2-SXMS 60383 60383