Development of Riemannian optimization algorithms and their applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 26887037
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science
• Principal Investigator: SATO Hiroyuki 東京理科大学, 工学部, 助教 (80734433)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: 最適化 / アルゴリズム / 応用数学 / 数理工学 / 幾何学

Outline of Final Research Achievements

Constrained optimization problems whose feasible sets are Riemannian manifolds can be regarded as unconstrained problems on the manifolds. Among nonlinear conjugate gradient methods on the Euclidean space, which are known as effective methods for large-scale problems, the Dai-Yuan-type method is guaranteed to have global convergence property under a mild assumption. This research generalized the Dai-Yuan-type method to that on Riemannian manifolds, which led to a novel Riemannian optimization algorithm. This research also proposed a new joint singular value decomposition algorithm based on the Riemannian trust-region method.

Free Research Field

最適化