Solution Methods For Minimizing A Class Of Clipped Functions

In this thesis,the minimization problem of a class of clipped functions is studied,which is widely and important used in position analysis,image processing,artificial intelligence and so on.In fact,this problem is a non-convex non-smooth NP-hard problem.Firstly,the clipped function is analyzed and its equivalent formulas are given,and the equivalent models of this kind of clipped function minimization problem are obtained.Secondly,four calculation methods for solving the problem are given by using the ideas of the heuristic algorithm,smooth approximation,ADMM algorithm and DC algorithm.Then,in order to illustrate the advantages of the clipped function minimization model,taking the empirical risk minimization problem as an example,we compare the clipped regression model,linear regression model and Huber regression model.Finally,we conduct numerical experiments on specific problems.The numerical experimental results show that the calculation methods given in this thesis are effective,and the performance of these four methods largely depends on the problem and simulation settings.