• DOI:10.1002/nla.2459
• Corpus ID: 244714599

Local convergence of alternating low-rank optimization methods with overrelaxation

@article{Oseledets2021LocalCO,
  title={Local convergence of alternating low-rank optimization methods with overrelaxation},
  author={I. Oseledets and Maxim V. Rakhuba and Andr{\'e} Uschmajew},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.14758}
}

• I. Oseledets, M. Rakhuba, A. Uschmajew
• Published 29 November 2021
• Mathematics
• ArXiv

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 2 × 2 block systems.