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Riemannian optimization and its applications / Hiroyuki Sato.

9783030623913 (electronic bk.)
3030623912 (electronic bk.)
3030623890
9783030623890

Cham, Switzerland : Springer, [2021]

English

1 online resource

10.1007/978-3-030-62391-3 doi

QA649 .S38 2021

516.373

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.

Includes bibliographical references and index.

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Online resource; title from digital title page (viewed on March 24, 2021).

SpringerBriefs in electrical and computer engineering. Control, automation and robotics.

Print version: 9783030623890

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