Abstract
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.
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Data Availability
The data used in this research is freely accessible. This can be downloaded at https://sparse.tamu.edu/.
Notes
The Riemannian gradient methods Cayley and Qgeodesic can be downloaded from https://github.com/opt-gaobin/spopt.
The SuiteSparse Matrix Collection tool-box is available in https://sparse.tamu.edu/.
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Acknowledgements
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.
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Oviedo, H., Herrera, R. A collection of efficient retractions for the symplectic Stiefel manifold. Comp. Appl. Math. 42, 164 (2023). https://doi.org/10.1007/s40314-023-02302-0
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DOI: https://doi.org/10.1007/s40314-023-02302-0