The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p <...The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11171299)
文摘The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.
