Local convergence of alternating low-rank optimization methods with overrelaxation

Abstract

The local convergence of alternating optimization methods with overrelaxation for lowrank 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.