Local convergence of alternating low-rank optimization methods with overrelaxation |
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Authors: | Ivan V Oseledets Maxim V Rakhuba André Uschmajew |
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Institution: | 1. Skolkovo Institute of Science and Technology, Moscow, Russia;2. HSE University, Moscow, Russia;3. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany |
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Abstract: | The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a positive semidefinite Hessian and can be studied in the corresponding quotient geometry of equivalent low-rank representations. In the matrix case, the optimal relaxation parameter for accelerating the local convergence can be determined from the convergence rate of the standard method. This result relies on a version of Young's SOR theorem for positive semidefinite block systems. |
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Keywords: | ALS low-rank optimization overrelaxation SOR method |
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