A smoothing proximal gradient algorithm for matrix rank minimization problem

In this paper, we study the low-rank matrix minimization problem, where loss function is convex but nonsmooth and penalty term defined by cardinality function. We first introduce an exact continuous relaxation, that is, both problems have same minimizers optimal value. particular, a class of lifted stationary points relaxed problem show any local minimizer must be point. addition, derive lower bound property for nonzero singular values point hence also problem. Then smoothing proximal gradient (SPG) algorithm proposed to find relaxation model. Moreover, it shown accumulating sequence generated SPG At last, numerical examples efficiency algorithm.