Abstract:

In this paper, we propose a modified proximal gradient method for solving a class of nonsmooth convex optimization problems, which arise in many contemporarystatistical and signal processing applications. The proposed method adopts a new scheme to construct the descent direction based on the proximal gradient method. It is proven that the modified proximal gradient method is Q-linearly convergent without the assumption of the strong convexity of the objective function. Some numerical experiments have been conducted to evaluate the proposed method eventually.