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 \begin{document}$ L_{t,*-\alpha F} $\end{document} with an integer \begin{document}$ t $\end{document} and parameter \begin{document}$ \alpha $\end{document} 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.