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
In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent wo...In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent work Goldfarb et al.(2013) to cope with more generic convex minimization. For the proposed method,both the separable objective functions and the auxiliary penalty terms are linearized. Provided that the separable objective functions belong to C1,1(Rn), we prove the O(1/?) arithmetical complexity of the new method. Some preliminary numerical simulations involving image processing and compressive sensing are conducted.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.
基金supported by National Natural Science Foundation of China(Grant Nos.11301055 and 11401315)Natural Science Foundation of Jiangsu Province(Grant No.BK2009397)the Fundamental Research Funds for the Central Universities(Grant No.ZYGX2013J103)
文摘In this paper, we develop a novel alternating linearization method for solving convex minimization whose objective function is the sum of two separable functions. The motivation of the paper is to extend the recent work Goldfarb et al.(2013) to cope with more generic convex minimization. For the proposed method,both the separable objective functions and the auxiliary penalty terms are linearized. Provided that the separable objective functions belong to C1,1(Rn), we prove the O(1/?) arithmetical complexity of the new method. Some preliminary numerical simulations involving image processing and compressive sensing are conducted.
