New Projectionalgorithm For Solving The Multiple-sets Split Feasibility Problem

The multiple-sets split feasibility problem is a generalization and extension of the split feasibility problem .which is an very important class of optimization problems .In real life , the multiple-sets split feasibility problem is extensive used physics and biology , image reconstruction and signal processing. It can be a model for many inverse problems of problem. For example, the multiple-sets split feasibility problem is applied to the inverse problem of intensity-modulated radiation therapy in the domain of physics and biology. In the domain of image reconstruction and signal processing, It can be a model for inverse problems, where constraints are imposed on the solutions, in the domain of a linear operator as well as in the operator's range. Some people to pay close attention to the multiple-sets split feasibility problem. They gives a number of method to solves the problem of the multiple-sets split feasibility, in which the project method is important and basic. structure of the algorithms is simple and feasibility is favorable. This article focuses on solving the multiple-sets split feasibility problem with projection method.This article basic on equivalent of solving the multiple-sets split feasibility problem and optimization problems , we transform the multiple-sets split feasibility problem into a linear variational inequality problem, and then use the projection and contraction method of variational inequalities to solve the multiple-sets split feasibility problem, and proof for the convergence of new algorithms.the new algorithms do not need to calculate the matrix inverse. and overcome weakness of do need to calculate the spectral radius of matrix . In the numerical experiments the new algorithms show that the faster convergence rate. It have favorable feasibility and stability for a variety of problems.This paper is divided into six chapters. The first chapter introduces the definition ,basic form, background of application , history and current situation of the multiple-sets split feasibility problem. and also it's researching background. The second chapter describe the required prior knowledge, includes basic definitions and theorem of involve in this article . The third chapter discusses equivalent problem of the split feasibility problem. The fourth chapter introduces the basic framework of contraction algorithm, The fifth chapter describe structure of new algorithm and proving of convergence. Chapter six carry out numerical experiments and makes some analysis about the experimental results.