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001 978-3-031-58909-6
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020 _a9783031589096
_9978-3-031-58909-6
024 7 _a10.1007/978-3-031-58909-6
_2doi
050 4 _aQA402.5-402.6
072 7 _aPBU
_2bicssc
072 7 _aMAT042000
_2bisacsh
072 7 _aPBU
_2thema
100 1 _aNoonan, Jack.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978021
245 1 0 _aHigh-Dimensional Optimization
_h[electronic resource] :
_bSet Exploration in the Non-Asymptotic Regime /
_cby Jack Noonan, Anatoly Zhigljavsky.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXI, 143 p. 161 illus., 159 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Optimization,
_x2191-575X
505 0 _aIntroduction -- Chapter 1 High-dimensional cubes, balls and spherically symmetric distributions -- Chapter 2 Space exploration: partial covering and quantization.
520 _aThis 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. .
650 0 _aMathematical optimization.
_965522
650 0 _aStochastic processes.
_976770
650 0 _aMathematics
_xData processing.
_965715
650 1 4 _aOptimization.
_965528
650 2 4 _aStochastic Processes.
_976770
650 2 4 _aComputational Mathematics and Numerical Analysis.
_966073
700 1 _aZhigljavsky, Anatoly.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978022
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031589089
776 0 8 _iPrinted edition:
_z9783031589102
830 0 _aSpringerBriefs in Optimization,
_x2191-575X
_978023
856 4 0 _uhttps://doi.org/10.1007/978-3-031-58909-6
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60383
_d60383