Cholesky QR-based retraction on the generalized Stiefel manifold

Hiroyuki Sato () and Kensuke Aihara
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Hiroyuki Sato: Kyoto University
Kensuke Aihara: Tokyo City University

Computational Optimization and Applications, 2019, vol. 72, issue 2, No 1, 293-308

Abstract: Abstract When optimizing on a Riemannian manifold, it is important to use an efficient retraction, which maps a point on a tangent space to a point on the manifold. In this paper, we prove a map based on the QR factorization to be a retraction on the generalized Stiefel manifold. In addition, we propose an efficient implementation of the retraction based on the Cholesky QR factorization. Numerical experiments show that the proposed retraction is more efficient than the existing one based on the polar factorization.

Keywords: Riemannian optimization; Generalized Stiefel manifold; Retraction; Cholesky QR factorization; 90C30; 65K05; 65F30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-018-0046-7

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