Riemannian Optimization and Its Applications
Springer Nature Switzerland
ISBN 978-3-030-62391-3
Standardpreis
Bibliografische Daten
eBook. PDF
2021
IX, 129 p. 15 illus., 12 illus. in color..
In englischer Sprache
Umfang: 129 S.
Verlag: Springer Nature Switzerland
ISBN: 978-3-030-62391-3
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: SpringerBriefs in Electrical and Computer Engineering SpringerBriefs in Control, Automation and Robotics
Produktbeschreibung
This brief describes the basics of Riemannian optimization-optimization on Riemannian manifolds-introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields.
To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.
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