The L 2/3 regularization is a nonconvex and nonsmooth optimization problem. Cao et al. (Cao et al. (2013) [15]) 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) [15]). 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.
In this paper, we present continuous iteratively reweighted least squares algorithm (CIRLS) for solving the linear models problem by convex relaxation, and prove the convergence of this algorithm. Under some conditions, we give an error bound for the algorithm. In addition, the numerical result shows the efficiency of the algorithm.
This paper presents an accurate and efficient algorithm for solving the generalized elastic net regularization problem with smoothed 0 penalty for recovering sparse vector. Finding the optimal solution to the unconstrained 0 minimization problem in the recovery of compressive sensed signals is an NP-hard problem. We proposed an iterative algorithm to solve this problem. We then prove that the algorithm is convergent based on algebraic methods. The numerical result shows the efficiency and the accuracy of the algorithm.
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