Lipschitz continuously smoothing accelerated proximal gradient method

This paper presents smoothing proximal gradient methods using smooth approximation that is Lipschitz continuous with respect to a smoothing parameter in a non-differentiable term in an objective function. Furthermore, an accelerated proximal gradient method exploiting the strong convexity of the objective function is proposed, and the convergence analysis using the estimate function technique results in explicit convergence rates and provides suitable criteria for choosing smoothing parameter sequences. The proposed framework points out that the acceleration based on the strong convexity improves theoretical convergence rate. From the viewpoint of the implementation, the proposed algorithms can be simply implemented on replacing the Lipschitz smoothness parameter in conventional algorithms with the proposed smoothing parameter sequence.