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MiS Preprint
29/2021

Local convergence of alternating low-rank optimization methods with overrelaxation

Ivan V. Oseledets, Maxim V. Rakhuba and André Uschmajew

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 $2 \times 2$ block systems.

Received:
Nov 29, 2021
Published:
Nov 29, 2021

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inJournal
2022 Repository Open Access
Ivan V. Oseledets, Maxim Rakhuba and André Uschmajew

Local convergence of alternating low-rank optimization methods with overrelaxation

In: Numerical linear algebra with applications, (2022)