Titlebook: Riemannian Optimization and Its Applications; Hiroyuki Sato Book 2021 The Author(s), under exclusive license to Springer Nature Switzerlan

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Book 2021blems, 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

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Introduction,nconstrained minimization problem on the unit sphere; this is one of the simplest examples of a Riemannian optimization problem. The steepest descent method on the sphere is also presented as an introduction to Riemannian optimization algorithms.

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Preliminaries and Overview of Euclidean Optimization,alculus, we review some aspects of these topics in consideration of their relationship to manifolds. One of our goals is to establish a foundation for discussion of Riemannian optimization; therefore, throughout this chapter, we note important information where appropriate.

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2191-8112 s some important applications including the eigenvalue and singular value decompositions in numericallinear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics..978-3-030-62389-0978-3-030-62391-3Series ISSN 2191-8112 Series E-ISSN 2191-8120

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Book 2021ptimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numericallinear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics..

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Hiroyuki Satoect. 4.8, the GENIVI Alliance., essential for telematic and infotainment components, is introduced. Section 4.9 provides examples of advanced driver assistance systems (ADASs) (see also Chap. .), and Sect. 4.10 looks at future trends. Section 4.11 contains a comprehensive set of questions on automot