L2/3 regularization: Convergence of iterative thresholding algorithm

Regularization: Convergence of Iterative Half Thresholding Algorithm

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, Lq regularization with q ∈ (0, 1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L1 regularization), however, the convergence issue of the corresponding algorithms are more difficult t...

Linear convergence of iterative soft-thresholding

In this article, the convergence of the often used iterative softthresholding algorithm for the solution of linear operator equations in infinite dimensional Hilbert spaces is analyzed in detail. We formulate the algorithm in the framework of generalized gradient methods and present a new convergence analysis. The analysis bases on new techniques like the Bregman-Taylor distance. As main result...

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

PArameter-free Generic Iterative Thresholding Algorithm (PAGITA)

The convergence guarantee of the iterative thresholding algorithm with suboptimal feedbacks for large systems

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be computationally expensive and/or prohibitive. The null space tuning algorithm with hard thresholding and feedbacks (NST+HT+FB) has a mean to expedite its procedure b...