TY - JOUR
T1 - A collection of efficient retractions for the symplectic Stiefel manifold
AU - Oviedo, H.
AU - Herrera, R.
N1 - Funding Information:
The first author was financially supported by the Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, through the FES startup package for scientific research. The second author was financially supported in part by CONACYT (Mexico), Grants 256126.
Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2023/6
Y1 - 2023/6
N2 - This article introduces a new map on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel retraction is a inversion of size 2p-by-2p, which is much less expensive than those required for the available retractions in the literature. Later, with the new retraction, we design a constraint preserving gradient method to minimize smooth functions defined on the symplectic Stiefel manifold. To improve the numerical performance of our approach, we use the non-monotone line-search of Zhang and Hager with an adaptive Barzilai–Borwein type step-size. Our numerical studies show that the proposed procedure is computationally promising and is a very good alternative to solve large-scale optimization problems over the symplectic Stiefel manifold.
AB - This article introduces a new map on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel retraction is a inversion of size 2p-by-2p, which is much less expensive than those required for the available retractions in the literature. Later, with the new retraction, we design a constraint preserving gradient method to minimize smooth functions defined on the symplectic Stiefel manifold. To improve the numerical performance of our approach, we use the non-monotone line-search of Zhang and Hager with an adaptive Barzilai–Borwein type step-size. Our numerical studies show that the proposed procedure is computationally promising and is a very good alternative to solve large-scale optimization problems over the symplectic Stiefel manifold.
KW - Riemannian gradient method
KW - Riemannian optimization
KW - Symplectic Stiefel manifold
KW - Symplectic matrix
UR - http://www.scopus.com/inward/record.url?scp=85156250346&partnerID=8YFLogxK
U2 - 10.1007/s40314-023-02302-0
DO - 10.1007/s40314-023-02302-0
M3 - Article
AN - SCOPUS:85156250346
SN - 2238-3603
VL - 42
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 4
M1 - 164
ER -