LOW RANK MATRIX MINIMIZATION WITH A TRUNCATED DIFFERENCE OF NUCLEAR NORM AND FROBENIUS NORM REGULARIZATION

In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form L-t,L-*-alpha F with an integer t and parameter a for rank minimization problem. The forward-backward splitting (FBS) algorithm is proposed to solve such a regularization problem, whose subproblems are shown to have closed-form solutions. We show that any accumulation point of the sequence generated by the FBS algorithm is a first-order stationary point. In the end, the numerical results demonstrate that the proposed FBS algorithm outperforms the existing methods.