On Globally Q-Linear Convergence of a Splitting Method for Group Lasso

In this paper, we discuss a splitting method for group Lasso. By assuming that the sequence of the step lengths has positive lower bound and positive upper bound (unrelated to the given problem data), we prove its Q-linear rate of convergence of the distance sequence of the iterates to the solution set. Moreover, we make comparisons with convergence of the proximal gradient method analyzed very recently. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany.