國立高雄大學圖資館 |

Language: English

Back

Population-based optimization on Riemannian manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	Population-based optimization on Riemannian manifoldsby Robert Simon Fong, Peter Tino.
Author:	Fong, Robert Simon.
other author:	Tino, Peter.
Published:	Cham :Springer International Publishing :2022.
Description:	xi, 168 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Riemannian manifolds.
Online resource:	https://doi.org/10.1007/978-3-031-04293-5
ISBN:	9783031042935$q(electronic bk.)

Population-based optimization on Riemannian manifolds
Fong, Robert Simon.

Population-based optimization on Riemannian manifolds[electronic resource] /by Robert Simon Fong, Peter Tino. - Cham :Springer International Publishing :2022. - xi, 168 p. :ill., digital ;24 cm. - Studies in computational intelligence,v. 10461860-9503 ;. - Studies in computational intelligence ;v. 216..

Introduction -- Riemannian Geometry: A Brief Overview -- Elements of Information Geometry -- Probability Densities on Manifolds.

Manifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold. Manifold optimization methods mainly focus on adapting existing optimization methods from the usual "easy-to-deal-with" Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However, to accommodate the adaptation process, assumptions on the search space manifold often have to be made. In addition, the computations and estimations are confined by the local geometry. This book presents a framework for population-based optimization on Riemannian manifolds that overcomes both the constraints of locality and additional assumptions. Multi-modal, black-box manifold optimization problems on Riemannian manifolds can be tackled using zero-order stochastic optimization methods from a geometrical perspective, utilizing both the statistical geometry of the decision space and Riemannian geometry of the search space. This monograph presents in a self-contained manner both theoretical and empirical aspects of stochastic population-based optimization on abstract Riemannian manifolds.

ISBN: 9783031042935$q(electronic bk.)

Standard No.: 10.1007/978-3-031-04293-5doiSubjects--Topical Terms:

190949
Riemannian manifolds.

LC Class. No.: QA649 / .F65 2022

Dewey Class. No.: 516.373

Population-based optimization on Riemannian manifolds
LDR:02557nmm a2200337 a 4500 001 621288
003 DE-He213
005 20220517154214.0
006 m d
007 cr nn 008maaau
008 221121s2022 sz s 0 eng d
020 $a 9783031042935$q(electronic bk.)
020 $a 9783031042928$q(paper)
024 7 $a 10.1007/978-3-031-04293-5 $2 doi
035 $a 978-3-031-04293-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA649 $b .F65 2022
072 7 $a UYQ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a UYQ $2 thema
082 0 4 $a 516.373 $2 23
090 $a QA649 $b .F674 2022
100 1 $a Fong, Robert Simon. $3 922392
245 1 0 $a Population-based optimization on Riemannian manifolds $h [electronic resource] / $c by Robert Simon Fong, Peter Tino.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xi, 168 p. : $b ill., digital ; $c 24 cm.
490 1 $a Studies in computational intelligence, $x 1860-9503 ; $v v. 1046
505 0 $a Introduction -- Riemannian Geometry: A Brief Overview -- Elements of Information Geometry -- Probability Densities on Manifolds.
520 $a Manifold optimization is an emerging field of contemporary optimization that constructs efficient and robust algorithms by exploiting the specific geometrical structure of the search space. In our case the search space takes the form of a manifold. Manifold optimization methods mainly focus on adapting existing optimization methods from the usual "easy-to-deal-with" Euclidean search spaces to manifolds whose local geometry can be defined e.g. by a Riemannian structure. In this way the form of the adapted algorithms can stay unchanged. However, to accommodate the adaptation process, assumptions on the search space manifold often have to be made. In addition, the computations and estimations are confined by the local geometry. This book presents a framework for population-based optimization on Riemannian manifolds that overcomes both the constraints of locality and additional assumptions. Multi-modal, black-box manifold optimization problems on Riemannian manifolds can be tackled using zero-order stochastic optimization methods from a geometrical perspective, utilizing both the statistical geometry of the decision space and Riemannian geometry of the search space. This monograph presents in a self-contained manner both theoretical and empirical aspects of stochastic population-based optimization on abstract Riemannian manifolds.
650 0 $a Riemannian manifolds. $3 190949
650 0 $a Mathematical optimization. $3 183292
650 1 4 $a Computational Intelligence. $3 338479
650 2 4 $a Artificial Intelligence. $3 212515
700 1 $a Tino, Peter. $3 922393
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Studies in computational intelligence ; $v v. 216. $3 380871
856 4 0 $u https://doi.org/10.1007/978-3-031-04293-5
950 $a Intelligent Technologies and Robotics (SpringerNature-42732)