Riemannian Optimization and Its Applications
Satō, Hiroyuki
Riemannian Optimization and Its Applications by Hiroyuki Sato - First edition 2021 - 1 recurso en línea (IX, 129 páginas) 15 ilustraciones, 12 ilustraciones a color - SpringerBriefs in Control Automation and Robotics 2192-6786 Intelligent Technologies and Robotics (SpringerNature-42732) Intelligent Technologies and Robotics (R0) (SpringerNature-43728) .
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.
9783030623913
10.1007/978-3-030-62391-3 doi
Variedades riemannianas
QA671 / 2021 EB
Riemannian Optimization and Its Applications by Hiroyuki Sato - First edition 2021 - 1 recurso en línea (IX, 129 páginas) 15 ilustraciones, 12 ilustraciones a color - SpringerBriefs in Control Automation and Robotics 2192-6786 Intelligent Technologies and Robotics (SpringerNature-42732) Intelligent Technologies and Robotics (R0) (SpringerNature-43728) .
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.
9783030623913
10.1007/978-3-030-62391-3 doi
Variedades riemannianas
QA671 / 2021 EB