Title :
Riemannian conjugate gradient method for complex singular value decomposition problem
Author_Institution :
Dept. of Manage. Sci., Tokyo Univ. of Sci., Tokyo, Japan
Abstract :
In this paper, a Riemannian conjugate gradient method for a Riemannian optimization problem related to the singular value decomposition of a complex matrix is developed. The proposed algorithm is globally convergent, unlike Newton´s method. However, Newton´s method for this problem is locally quadratically convergent. With this in mind, the proposed conjugate gradient method is combined with Newton´s method to produce a hybrid algorithm, which is globally and quadratically convergent in practice.
Keywords :
Newton method; conjugate gradient methods; optimisation; singular value decomposition; Newton method; Riemannian conjugate gradient method; Riemannian optimization problem; SVD; complex matrix; complex singular value decomposition problem; hybrid algorithm; Equations; Gradient methods; Manifolds; Matrix decomposition; Newton method; Vectors;
Conference_Titel :
Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on
Conference_Location :
Los Angeles, CA
Print_ISBN :
978-1-4799-7746-8
DOI :
10.1109/CDC.2014.7040305
