Linearized Augmented Lagrangian Method For Sparse Solution Of Underdetermined Linear Equations

In this paper, we consider to find the sparest solution of the large underdetermined system of linear equations y = Ax with nonnegative constraint x ≥ 0. Such problems are frequently encountered in signal and image processing, in handling of multispectral data, considering nonnegative factorization for recognition. Based on the classical augmented Lagrangian method, we propose an efficient linearized augmented Lagrangian method for this problem. The convergence theorem of the proposed method is given. Experimental results are given to illustrate feasibility and effectiveness of our method.