03604nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072001700183072002300200072001500223072001600238100007700254245011100331250001800442264006900460300006500529336002600594337002600620338003600646347002400682490003600706505023000742520173100972650002502703650003102728650002502759650004502784650001802829650002502847710003402872773002602906776003602932776003602968776003603004830003603040856004603076978-3-031-67422-8DE-He21320251030113240.0cr nn 008mamaa241023s2024    sz |    s    |||| 0|eng d  a97830316742287 a10.1007/978-3-031-67422-82doi 4aT57.6-.97 7aKJT2bicssc 7aKJMD2bicssc 7aBUS0490002bisacsh 7aKJT2thema 7aKJMD2thema1 aJahn, Johannes.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aOrder Analysis, Deep Learning, and Connections to Optimizationh[electronic resource] /cby Johannes Jahn.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIX, 181 p. 64 illus., 63 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aVector Optimization,x1867-898X0 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.  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. 0aOperations research. 0aMathematical optimization. 0aFunctional analysis.14aOperations Research and Decision Theory.24aOptimization.24aFunctional Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303167421108iPrinted edition:z978303167423508iPrinted edition:z9783031674242 0aVector Optimization,x1867-898X40uhttps://doi.org/10.1007/978-3-031-67422-8