Convergence analysis of the augmented Lagrange multiplier algorithm for a class of matrix compressive recovery

In this paper, we mainly discuss the convergence of the augmented Lagrange multiplier (ALM) algorithm for matrix compressive recovery presented in Wright et al. (2013). Because of the unknown ∂‖PΩ(A)‖∗∂‖PΩ(A)‖∗, it is hard to obtain the convergence. So we convert the model in Wright et al. (2013) to the equivalent model in Meng et al. (2014), and discuss the convergence of the ALM algorithm for the model in Meng et al. (2014). Finally, the numerical experiments show the convergence of the ALM algorithm for the matrix compressive recovery.