In this talk,we present a novel multi-step inertial Forward—Backward splitting method for the minimization of the sum of two functions,one of which is proper convex and lower semi-continuous,while the other one is convex differentiable with gradient being Lipschitz continuous.The proposed method covers several existing work(e.g.onestep inertial Forward—Backward splitting,and FISTA)as special cases,and global convergence is provided.We also illustrate the advantage of using multiple inertial steps.Various numerical experiments arising from image processing and machine learning are considered to demonstrate the advantage of the proposed method.