Low rank matrix minimization with a truncated difference of nuclear norm and Frobenius norm regularization

Abstract

<p style='text-indent:20px;'>In this paper, we present a novel regularization with a truncated difference of nuclear norm and Frobenius norm of form <inline-formula><tex-math id="M1">\begin{document}$ L_{t,*-\alpha F} $\end{document}</tex-math></inline-formula> with an integer <inline-formula><tex-math id="M2">\begin{document}$ t $\end{document}</tex-math></inline-formula> and parameter <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> 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.</p>