Proximal iteratively reweighted algorithm for low-rank matrix recovery

Abstract

This paper proposes a proximal iteratively reweighted algorithm to recover a low-rank matrix based on the weighted fixed point method. The weighted singular value thresholding problem gains a closed form solution because of the special properties of nonconvex surrogate functions. Besides, this study also has shown that the proximal iteratively reweighted algorithm lessens the objective function value monotonically, and any limit point is a stationary point theoretically.