Sparse Regularization: Convergence Of Iterative Jumping Thresholding Algorithm

Abstract

In recent studies on sparse modeling, nonconvex penalties have received considerable attentions due to their superiorities on sparsity-inducing over the convex counterparts. In this paper, we study the convergence of a nonconvex iterative thresholding algorithm for solving a class of sparse regularized optimization problems, where the corresponding thresholding functions of the penalties are discontinuous with jump discontinuities. Therefore, we call the algorithm the iterative jumping thresholding (IJT) algorithm. The finite support and sign convergence of IJT algorithm is first verified via taking advantage of such jump discontinuity. Together with the introduced restricted Kurdyka–Łojasiewicz property, then the global convergence 1 1 The global convergence in this paper is defined in the sense that the entire sequence converges regardless of the initial point.