Adaptive Localized Cayley Parametrization for Optimization Over Stiefel Manifold and Its Convergence Rate Analysis
The Adaptive Localized Cayley Parametrization (ALCP) strategy for orthogonality constrained optimization has been proposed as a scheme to utilize Euclidean optimization algorithms on an adaptive parametrization of the Stiefel manifold via a tunable generalized left-localized Cayley parametrization....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2024-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10443428/ |
| Summary: | The Adaptive Localized Cayley Parametrization (ALCP) strategy for orthogonality constrained optimization has been proposed as a scheme to utilize Euclidean optimization algorithms on an adaptive parametrization of the Stiefel manifold via a tunable generalized left-localized Cayley parametrization. Thanks to the adaptive parametrization, the ALCP strategy enjoys stable convergence of the estimate sequence of a minimizer by avoiding a certain singular-point issue. In this paper, we present a convergence rate analysis for the ALCP strategy using Euclidean optimization algorithms such as Nesterov-type accelerated gradient methods. Numerical experiments demonstrate the effectiveness of the ALCP strategy. |
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| ISSN: | 2169-3536 |