In this paper, we consider a class of nonsmooth problem that is the sum of a Lipschitz differentiable function and a nonsmooth and proper lower semicontinuous function. We discuss here the convergence rate of the function values for a nonmonotone accelerated proximal gradient method, which proposed in "Huan Li and Zhouchen Lin: Accelerated proximal gradient methods for nonconvex programming" for the nonconvex case but with incomplete theoretical analysis. Further, we proposed a hybrid proximal gradient method for the nonconvex setting and show the corresponding theoretical analysis under the assumption that objective function has the Kurdyka-Lojasiewicz property. Numerical experiments on nonconvex models to demonstrate the advantage of the proposed method.
View On the Convergence Results of a class of Nonmonotone Accelerated Proximal Gradient Methods for Nonsmooth and Nonconvex Minimization Problems