03958nam a22005655i 4500 978-3-031-67422-8 DE-He213 20251030113240.0 cr nn 008mamaa 241023s2024 sz | s |||| 0|eng d 9783031674228 978-3-031-67422-8 10.1007/978-3-031-67422-8 doi T57.6-.97 KJT bicssc KJMD bicssc BUS049000 bisacsh KJT thema KJMD thema Jahn, Johannes. author. aut http://id.loc.gov/vocabulary/relators/aut 86448 Order Analysis, Deep Learning, and Connections to Optimization [electronic resource] / by Johannes Jahn. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIX, 181 p. 64 illus., 63 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Vector Optimization, 1867-898X Preliminaries -- 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. This 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. Operations research. 57943 Mathematical optimization. 65522 Functional analysis. Operations Research and Decision Theory. 67143 Optimization. 65528 Functional Analysis. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031674211 Printed edition: 9783031674235 Printed edition: 9783031674242 Vector Optimization, 1867-898X 86449 https://doi.org/10.1007/978-3-031-67422-8 ZDB-2-BUM ZDB-2-SXBM 64409 64409