Local convergence of alternating low-rank optimization methods with overrelaxation

Ivan V. Oseledets; Maxim V. Rakhuba; André Uschmajew

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arXiv · 2111.14758

Local convergence of alternating low-rank optimization methods with overrelaxation

Ivan V. Oseledets·Maxim V. Rakhuba·André Uschmajew

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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 $2 \times 2$ block systems.

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Ivan V. Oseledets, Maxim V. Rakhuba, André Uschmajew. 2021-11-29. Local convergence of alternating low-rank optimization methods with overrelaxation. https://arxiv.org/abs/2111.14758

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