L2/3 regularization: Convergence of iterative thresholding algorithm

The L-2/3 regularization is a nonconvex and nonsmooth optimization problem. Cao et al. (2013) investigated that the L-2/3 regularization is more effective in imaging deconvolution. The convergence issue of the iterative thresholding algorithm of L-2/3 regularization problem (the L-2/3 algorithm) hasn't been addressed in Cao et al. (2013). In this paper, we study the convergence of the L-2/3 algorithm. As the main result, we show that under certain conditions, the sequence {X-(n)} generated by the L-2/3 algorithm converges to a local minimizer of L-2/3 regularization, and its asymptotical convergence rate is linear. We provide a set of experiments to verify our theoretical assertions and show the performance of the algorithm on sparse signal recovery. The established results provide a theoretical guarantee for a wide range of applications of the algorithm. (C) 2015 Elsevier Inc. All rights reserved.