In this paper, we propose an efficient adaptive iteratively reweighted l1 algorithm (A-IRL1 algorithm) for solving the elastic lq regularization problem. We prove that the sequence generated by the A-IRL1 algorithm is convergent for any rational and the limit is a critical point of the elastic lq regularization problem. Under certain conditions, we present an error bound for the limit point of convergent sequence.
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and the limit is a critical point of the elastic 
