Homotopy Method For Matrix Rank Minimization Based On The Matrix Hard Thresholding Method

Based on the matrix hard thresholding method, a homotopy method is proposed for solving the matrix rank minimization problem. This method iteratively solves a series of regularization subproblems, whose solutions are given in closed form by the matrix hard thresholding operator. Under some mild assumptions, convergence of the proposed method is proved. The proposed method does not depend on a prior knowledge of exact rank value. Numerical experiments demonstrate that the proposed homotopy method weakens the affection of the choice of the regularization parameter, and is more efficient and effective than the existing sate-of-the-art methods.