リーマン最適化と応用 Riemannian Optimization and Its Applications (Springerbriefs in Control, Automation and Robotics)

Sato, Hiroyuki

Springer Nature Switzerland AG（2021/02発売）

Springer Nature Switzerland AG（2021/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 129 p.
• 言語 ENG
• 商品コード 9783030623890

Full Description

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 numericallinear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.

Contents

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.