LEADER 03764nam 22006015 450 001 9910897979803321 005 20250808090430.0 010 $a9783031674228 010 $a3031674227 024 7 $a10.1007/978-3-031-67422-8 035 $a(MiAaPQ)EBC31738047 035 $a(Au-PeEL)EBL31738047 035 $a(CKB)36389222100041 035 $a(OCoLC)1465009324 035 $a(DE-He213)978-3-031-67422-8 035 $a(EXLCZ)9936389222100041 100 $a20241023d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOrder Analysis, Deep Learning, and Connections to Optimization /$fby Johannes Jahn 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (189 pages) 225 1 $aVector Optimization,$x1867-898X 311 08$a9783031674211 311 08$a3031674219 327 $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. 330 $aThis book introduces readers to order analysis and various aspects of deep learning, and describes important connections to optimization, such as nonlinear optimization as well as vector and set optimization. Besides a review of the essentials, this book consists of two main parts. The first main part focuses on the introduction of order analysis as an application-driven theory, which allows to treat order structures with an analytical approach. Applications of order analysis to nonlinear optimization, as well as vector and set optimization with fixed and variable order structures, are discussed in detail. This means there are close ties to finance, operations research, and multicriteria decision making. Deep learning is the subject of the second main part of this book. In addition to the usual basics, the focus is on gradient methods, which are investigated in the context of complex models with a large number of parameters. And a new fast variant of a gradient method is presented in this part. Finally, the deep learning approach is extended to data sets given by set-valued data. Although this set-valued approach is more computationally intensive, it has the advantage of producing more robust predictions. This book is primarily intended for researchers in the fields of optimization, order theory, or artificial intelligence (AI), but it will also benefit graduate students with a general interest in these fields. The book assumes that readers have a basic understanding of functional analysis or at least basic analysis. By unifying and streamlining existing approaches, this work will also appeal to professionals seeking a comprehensive and straightforward perspective on AI or order theory approaches. 410 0$aVector Optimization,$x1867-898X 606 $aOperations research 606 $aMathematical optimization 606 $aFunctional analysis 606 $aOperations Research and Decision Theory 606 $aOptimization 606 $aFunctional Analysis 615 0$aOperations research. 615 0$aMathematical optimization. 615 0$aFunctional analysis. 615 14$aOperations Research and Decision Theory. 615 24$aOptimization. 615 24$aFunctional Analysis. 676 $a515 700 $aJahn$b Johannes$0374159 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897979803321 996 $aOrder Analysis, Deep Learning, and Connections to Optimization$94211504 997 $aUNINA