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Riemannian optimization and its appl...

Sato, Hiroyuki.

Riemannian optimization and its applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Riemannian optimization and its applicationsby Hiroyuki Sato.
Author:	Sato, Hiroyuki.
Published:	Cham :Springer International Publishing :2021.
Description:	ix, 129 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Riemannian manifolds.
Online resource:	https://doi.org/10.1007/978-3-030-62391-3
ISBN:	9783030623913$q(electronic bk.)

Riemannian optimization and its applications
Sato, Hiroyuki.

Riemannian optimization and its applications[electronic resource] /by Hiroyuki Sato. - Cham :Springer International Publishing :2021. - ix, 129 p. :ill., digital ;24 cm. - SpringerBriefs in electrical and computer engineering, Control, automation and robotics. - SpringerBriefs in electrical and computer engineering.Control, automation and robotics..

Chapter 1. Introduction -- Chapter 2. Preliminaries and Overview of Euclidean Optimization -- Chapter 3. Unconstrained Optimization on Riemannian Manifolds -- Chapter 4. Conjugate Gradient Methods on Riemannian Manifolds -- Chapter 5. Applications of Riemannian Optimization -- Chapter 6. Recent Developments in Riemannian Optimization.

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.

ISBN: 9783030623913$q(electronic bk.)

Standard No.: 10.1007/978-3-030-62391-3doiSubjects--Topical Terms:

190949
Riemannian manifolds.

LC Class. No.: QA649 / .S38 2021

Dewey Class. No.: 516.373

Riemannian optimization and its applications
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520 $a 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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