Matrix completion via a low rank factorization model and an Augmented Lagrangean Succesive Overrelaxation Algorithm

Abstract

The matrix completion problem (MC) has been approximated by using the nuclear norm relaxation. Some algorithms based on this strategy require the computationally expensive singular value decomposition (SVD) at each iteration. One way to avoid SVD calculations is to use alternating methods, which pursue the completion through matrix factorization with a low rank condition. In this work an augmented Lagrangean-type alternating algorithm is proposed. The new algorithm uses duality information to define the iterations, in contrast to the solely primal LMaFit algorithm, which employs a Successive Over Relaxation scheme. The convergence result is studied. Some numerical experiments are given to compare numerical performance of both proposals.

Keywords

• matrix completion
• alternanting minimization
• nonlinear Gauss-Seidel method
• nonlinear SOR method
• Augmented Lagrange method