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In this paper, we propose an iteratively reweightedminimization algorithm (IRL1 algorithm) for solving the elasticminimization problem. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We also prove that the sequence is convergent for any rationaland the limit is a stationary point of the elasticminimization problem. Moreover, under certain conditions, we present an error bound between the limit point of convergent sequence and the sparse solution of underdetermined linear system. Numerical experiments on sparse vector recovery are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms: we derive a Lagrange–Newton algorithm for the nonsmooth convex optimization, and establish the nonsingularity of the Newton system and the local convergence of the algorithm. [ABSTRACT FROM PUBLISHER]