國立虎尾科技大學 |

Riemannian Optimization and Its Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Riemannian Optimization and Its Applications/ by Hiroyuki Sato.
作者:	Sato, Hiroyuki.
面頁冊數:	IX, 129 p. 15 illus., 12 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Linear and Multilinear Algebras, Matrix Theory. -
電子資源:	https://doi.org/10.1007/978-3-030-62391-3
ISBN:	9783030623913

Riemannian Optimization and Its Applications
Sato, Hiroyuki.

Riemannian Optimization and Its Applications[electronic resource] /by Hiroyuki Sato. - 1st ed. 2021. - IX, 129 p. 15 illus., 12 illus. in color.online resource. - SpringerBriefs in Control, Automation and Robotics,2192-6794. - SpringerBriefs in Control, Automation and Robotics,.

Introduction -- Preliminaries and Overview of Euclidean Optimization -- Unconstrained Optimization on Riemannian Manifolds -- Conjugate Gradient Methods on Riemannian Manifolds -- Applications of Riemannian Optimization -- 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

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

672090
Linear and Multilinear Algebras, Matrix Theory.

LC Class. No.: TJ212-225

Dewey Class. No.: 629.8

Riemannian Optimization and Its Applications
LDR:02728nam a22003975i 4500 001 1053447
003 DE-He213
005 20210920215326.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030623913 $9 978-3-030-62391-3
024 7 $a 10.1007/978-3-030-62391-3 $2 doi
035 $a 978-3-030-62391-3
050 4 $a TJ212-225
072 7 $a TJFM $2 bicssc
072 7 $a TEC004000 $2 bisacsh
072 7 $a TJFM $2 thema
082 0 4 $a 629.8 $2 23
100 1 $a Sato, Hiroyuki. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1289067
245 1 0 $a Riemannian Optimization and Its Applications $h [electronic resource] / $c by Hiroyuki Sato.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a IX, 129 p. 15 illus., 12 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Control, Automation and Robotics, $x 2192-6794
505 0 $a Introduction -- Preliminaries and Overview of Euclidean Optimization -- Unconstrained Optimization on Riemannian Manifolds -- Conjugate Gradient Methods on Riemannian Manifolds -- Applications of Riemannian Optimization -- Recent Developments in Riemannian Optimization.
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.
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 672090
650 2 4 $a Systems Theory, Control. $3 669337
650 2 4 $a Statistical Theory and Methods. $3 671396
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 1 4 $a Control and Systems Theory. $3 1211358
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Matrix theory. $3 1023862
650 0 $a System theory. $3 566168
650 0 $a Statistics . $3 1253516
650 0 $a Calculus of variations. $3 527927
650 0 $a Control engineering. $3 1249728
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030623890
776 0 8 $i Printed edition: $z 9783030623906
830 0 $a SpringerBriefs in Control, Automation and Robotics, $x 2192-6786 $3 1254578
856 4 0 $u https://doi.org/10.1007/978-3-030-62391-3
912 $a ZDB-2-INR
912 $a ZDB-2-SXIT
950 $a Intelligent Technologies and Robotics (SpringerNature-42732)
950 $a Intelligent Technologies and Robotics (R0) (SpringerNature-43728)