On The Proximal Gradient Method For Minimizing The Sum Of Two Functions

In this dissertation,we consider the convergence analysis of proximal gradient method for minimizing the sum of two functions.This dissertation,constructed by four parts,is organized as follows:In chapters 1 and 2,the backgrounds of this dissertation are introduced and some preliminaries are provided.In chapter 3,we investigate the convergence of inertial proximal gradient method(IPGM)for minimizing the sum of a nonsmooth convex function and a smooth nonconvex function.Under the assumption that the associated function satisfies the Kurdyka-Lojasiewicz inequality,we prove that the iterative sequence generated by the IPGM converges to a critical point of the problem.In chapter 4,we give a simple proof of the complexity analysis of fast proximal gradient method for minimizing the sum of two convex functions,where one of the involved function is smooth.