Researches On Splitting Methods With Inertial Term For Monotone Inclusions Problems

Monotone inclusion problems are one of the most basic problems in the fields of optimization and control,the operator splitting methods are the most basic and effective methods for solving this kind of problems.The forward-backward splitting method,Tseng’s splitting method and the DR splitting method and so on are the most popular methods for solving them.They are widely used in image processing,compressed sensing,finance,management and information science,which also promote the development and innovation of the splitting method along with the in-depth study of these practical problems.Firstly,Chapter 2 of this thesis focuses on the issue of adding inertial terms to the splitting method for monotone inclusion problems of three operators in real infinite-dimensional Hilbert space.Under appropriate assumptions,we analyze the weak convergence of the resulting algorithm.And it can also be applied to solving linear programming,semi-definite programming and convex minimization problems.Secondly,Chapter 3 deals with a class of convex minimization problems and discusses the weak convergence of an inertial operator splitting method.Finally,numerical experiments in Chapter 4 show the necessity of introducing inertial terms in order to improve the numerical performance.