New Projection Algorithm For Solving The Multiple-sets Split Feasibility Problem

The split feasibility problem is a very important class of optimization problems. Themultiple-sets split feasibility problem is a generalization and extension of the split feasibilityproblem. The multiple-sets split feasibility problem is extensive use biology, military and physics,image reconstruction and language processing system.moreover, It can be a model for manyinverse problems of problem, such as the intensity-modulated radiation therapy in the domain ofbiology. In order to solve this problem, they gives a great deal of method to solves the problem ofthe multiple-sets split feasibility. For example, use multiple range of the thought to solve theproblem of the split feasibility,the project method is important and basic. Due to the projectionalgorithm convenient construction, feasibility, now has formed a lot of projection algorithmeffectively, This article focuses on solving the split feasibility problem with projection method.Based on the predecessors of projection algorithm was studied, In this paper, the originalalgorithm is improved and then proved the convergence of the improved algorithm. the newalgorithms do not need to calculate the inverse of matrix and overcome weakness of do need tocalculate the spectral radius of matrix. compared the new algorithm and the original algorithm in thenumerical experiment, the results show that the new algorithms has the feasibility and stability for avariety of problems.This paper mainly has six chapters.First of all,introduces the definition of the multiple-setssplit feasibility problem, background of application, history and current situation of themultiple-sets split feasibility problem, The second chapter describe the required of basic knowledge,The third chapter discusses the application of variational inequalities in split feasibility problem.The fourth chapter described structure of new algorithm and proving of convergence. The fivechapter carry out numerical experiments and makes some analysis about the experimental results.The last Chapter is Summary and Outlook.