TY  - GEN
AB  - 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.
AU  - Sato, Hiroyuki,
CN  - QA649
DO  - 10.1007/978-3-030-62391-3
DO  - doi
ID  - 1434107
KW  - Riemannian manifolds.
KW  - Mathematical optimization.
KW  - Variétés de Riemann.
KW  - Optimisation mathématique.
LK  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-62391-3
N2  - 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.
SN  - 9783030623913
SN  - 3030623912
T1  - Riemannian optimization and its applications /
TI  - Riemannian optimization and its applications /
UR  - https://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-62391-3
ER  -