Study On Successive DC Approximation Method For Nonsmooth Nonconvex Problem

In this paper,we study a successive difference-of-convex approximation method for a class of nonsmooth nonconvex problems.The objective is the sum of a smooth function and a finite number of nonnegative proper nonsmooth nonconvex closed func-tions,and some of these functions are composed with linear maps.This kind of prob-lems arises from machine learning,etc.We propose a successive difference-of-convex approximation method to solve it.More specifically,we design a sequence of functions,which can approximate the original nonsmooth nonconvex functions asymptotically.Then,we minimize the resulting approximation function by applying nonmonotone proximal gradient method.Under certain assumptions,the sequence generated by this method is bounded,and any accumulation point of the sequence is a stationary point of the original problem.We apply the proposed method to two specific concrete appli-cations,and compare it with some other state-of-the-art algorithms to verify its conver-gence.