Local convergence of alternating low-rank optimization methods with\n overrelaxation

2021/11/29 by Ivan Oseledets, Oseledets, Ivan V., Maxim Rakhuba +3
Engineering · Computer Science · #Sparse and Compressive Sensing Techniques #Advanced Image Processing Techniques #Advanced Vision and Imaging

paper · pdf · doi:10.48550/arxiv.2111.14758

Abstract

The local convergence of alternating optimization methods with overrelaxation\nfor low-rank matrix and tensor problems is established. The analysis is based\non the linearization of the method which takes the form of an SOR iteration for\na positive semidefinite Hessian and can be studied in the corresponding\nquotient geometry of equivalent low-rank representations. In the matrix case,\nthe optimal relaxation parameter for accelerating the local convergence can be\ndetermined from the convergence rate of the standard method. This result relies\non a version of Young's SOR theorem for positive semidefinite 2 \× 2\nblock systems.\n

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