Accelerate randomized coordinate descent iterative hard thresholding methods for ℓ0 regularized convex problems

In this paper, we develop an accelerated random block coordinate descent iterative hard thresholding method (ARCD-IHT) for the minimization of ℓ
₀
regularized optimization problems, i.e. the objective function is the sum of a smooth convex function and the ℓ
₀
regularization. We first analyze random block coordinate descent iterative hard thresholding methods (RCD-IHT) which cover random proximal coordinate descent methods and random block-coordinate gradient descent methods. The random block coordinate descent iterative hard thresholding methods transform the minimization of ℓ
₀
regularized optimization problem to a smooth convex minimization problem. Then we apply the accelerated technique proposed in [2] to accelerate the RCD-IHT (ARCD-IHT). Numerical examples demonstrate that our algorithm performs favorably compared to the algorithm in [1].