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Population-based optimization on Rie...

Fong, Robert Simon.

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Population-based optimization on Riemannian manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	Population-based optimization on Riemannian manifolds/ by 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.
[NT 15003449]:	Introduction -- Riemannian Geometry: A Brief Overview -- Elements of Information Geometry -- Probability Densities on Manifolds.
Contained By:	Springer Nature eBook
Subject:	Riemannian manifolds. -
Online resource:	https://doi.org/10.1007/978-3-031-04293-5
ISBN:	9783031042935

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. 1046..

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

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

540526
Riemannian manifolds.

LC Class. No.: QA649 / .F65 2022

Dewey Class. No.: 516.373

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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.
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