Riemannian optimization and its applications / Hiroyuki Sato.
Sato, Hiroyuki, author.
2021
QA649 .S38 2021
Available Online

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Title Riemannian optimization and its applications / Hiroyuki Sato.
Author Sato, Hiroyuki, author.
ISBN 9783030623913 (electronic bk.)
3030623912 (electronic bk.)
3030623890
9783030623890
DOI https://doi.org/10.1007/978-3-030-62391-3
Published Cham, Switzerland : Springer, [2021]
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-62391-3 doi
Call Number QA649 .S38 2021
Dewey Decimal Classification 516.373
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from digital title page (viewed on March 24, 2021).
Series SpringerBriefs in electrical and computer engineering. Control, automation and robotics.
Available in Other Form Print version: 9783030623890
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Chapter 1. Introduction
Chapter 2. Unconstrained Optimization on Riemannian Manifolds
Chapter 3. Conjugate Gradient Methods on Manifolds
Chapter 4. Applications of Riemannian Optimization.

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