CONVERGENCE ANALYSIS OF PROXIMAL GRADIENT ALGORITHM WITH EXTRAPOLATION FOR A CLASS OF CONVEX NONSMOOTH MINIMIZATION PROBLEMS

In this paper, we consider the proximal gradient algorithm with extrapolation (PG(e)) for solving a class of nonsmooth convex minimization problems, whose objective function in the sum of a continuously differentiable convex function with Lipschitz gradient and a proper closed convex function. We first establish the subsequential convergence of iterate generated by PG(e), then we prove that the convergence rate of objective function is O (1/k), which implies that the convergence rate of FISTA with fixed restart is also O (1/k). Finally , we conduct some numerical experiments to illustrate the theoretical results