Low-rank and sparse matrix recovery via inexact Newton-like method with non-monotone search

Abstract

In this paper, a non-convex optimization model of the low-rank and sparse matrix recovery from partial samples is proposed, and an inexact Newton-like algorithm with non-monotone scheme for solving the non-convex optimization model is suggested, in which the inexact Newton-like algorithm is used for the low-rank matrix part and the non-monotone scheme is used for sparse matrix part. It is proved that the iterative sequence of the new algorithm converges to a stationary point of the model. Finally, numerical experiments show that the proposed algorithm is far superior to the missing low-rank sparse decomposition (MLSD) algorithm in Azghani et al., 2019 and Algorithm 1 in Gu et al., 2016 in CPU time, which indicates that the new algorithm is more efficient.