Further Results On Douglas-Rachford Splitting Method For Convex Minimization

In this paper, we study convex minimization problem and the corresponding Douglas-Rachford splitting method. They have been widely used in the fields of picture process-ing, compressed sensing, finance, management and information science, which promote the development and innovation of Douglas-Rachford splitting method along with the in-depth study of these practical problems.This thesis falls into three chapters and main content are as follows.In the first chapter, we briefly introduce Douglas-Rachford splitting method for convex minimization and also present preliminary results. In addition, we give the key points of the paper.In the second chapter, we make two-fold contributions, the first is that we discuss Douglas-Rachford splitting method for convex minimization if both f and g in the ob-jective function are closed, proper convex, and the gradient of f is Lipschitz continuous, then the method’s convergence is analyzed under weaker conditions on proximal param-eters. The second is that Douglas-Rachford splitting method for convex minimization involving nonzero bounded linear operators is considered, and it can be executed in-dependently, especially an advantage over many existing methods is their capability of processing the set-valued operators separately. In this paper, we give another possible form of Douglas-Rachford splitting method, and analyze its convergence.In the third chapter, we give some applications of our proposed methods to some practical problem.