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020 _a9783031674228
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024 7 _a10.1007/978-3-031-67422-8
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050 4 _aT57.6-.97
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072 7 _aKJMD
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100 1 _aJahn, Johannes.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986448
245 1 0 _aOrder Analysis, Deep Learning, and Connections to Optimization
_h[electronic resource] /
_cby Johannes Jahn.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIX, 181 p. 64 illus., 63 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 _aVector Optimization,
_x1867-898X
505 0 _aPreliminaries -- C Representing Functionals -- Application in Nonlinear Optimization -- Application in Vector Optimization -- Application in Set Optimization -- Basics of Deep Learning -- Deep Learning with Set-Valued Inputs.
520 _aThis book introduces readers to order analysis and various aspects of deep learning, and describes important connections to optimization, such as nonlinear optimization as well as vector and set optimization. Besides a review of the essentials, this book consists of two main parts. The first main part focuses on the introduction of order analysis as an application-driven theory, which allows to treat order structures with an analytical approach. Applications of order analysis to nonlinear optimization, as well as vector and set optimization with fixed and variable order structures, are discussed in detail. This means there are close ties to finance, operations research, and multicriteria decision making. Deep learning is the subject of the second main part of this book. In addition to the usual basics, the focus is on gradient methods, which are investigated in the context of complex models with a large number of parameters. And a new fast variant of a gradient method is presented in this part. Finally, the deep learning approach is extended to data sets given by set-valued data. Although this set-valued approach is more computationally intensive, it has the advantage of producing more robust predictions. This book is primarily intended for researchers in the fields of optimization, order theory, or artificial intelligence (AI), but it will also benefit graduate students with a general interest in these fields. The book assumes that readers have a basic understanding of functional analysis or at least basic analysis. By unifying and streamlining existing approaches, this work will also appeal to professionals seeking a comprehensive and straightforward perspective on AI or order theory approaches.
650 0 _aOperations research.
_957943
650 0 _aMathematical optimization.
_965522
650 0 _aFunctional analysis.
650 1 4 _aOperations Research and Decision Theory.
_967143
650 2 4 _aOptimization.
_965528
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031674211
776 0 8 _iPrinted edition:
_z9783031674235
776 0 8 _iPrinted edition:
_z9783031674242
830 0 _aVector Optimization,
_x1867-898X
_986449
856 4 0 _uhttps://doi.org/10.1007/978-3-031-67422-8
912 _aZDB-2-BUM
912 _aZDB-2-SXBM
999 _c64409
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