Research Of Algorithm For Solving The Multiple-sets Split Feasibility Problem

Multiple-sets split feasibility problem is an important class of optimization problems which is draw From the image reconstruction and signal processing areas such as abstract mathematical models, so the multiple-sets split feasibility problem plays a particularly crucial role in Image and signal processing efficiency. People have made a number of methods to solve the multiple-sets split feasibility problem, in which the projection method is a basic and important kind of way. Compare with other algorithms, projection method is constructed simply and can be implemented easily. On the basis of a large number of studies, many effective projection-like algorithms has been formed. This article focuses on solving the split feasibility problem with projection method.In this article 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. By joining the adaptive factor and using a different step size selection strategy, in each iteration the step length is automatically adjusted, making iterative steps to keep within a reasonable range. So the algorithm has good adaptability. The algorithms do not need to calculate the spectral radius of matrix and do not need to calculate the matrix inverse. This may improve the efficiency of the algorithms in time. In the numerical experiments the new algorithms are compared with the CQ algorithm and the numerical results show that the designed method can have faster convergence rate for a variety of problems. With the dimension of the problem increases, the performance was more obvious.This paper is divided into five chapters. The first chapter introduces the basic form and the application of the multiple-sets split feasibility problem and also it's researching background. The second chapter includes the required prior knowledge, transforms the split feasibility problem into a linear variational inequality. The third chapter describes the basic framework of projection . The fourth chapter introduces the several algorithms to solve MSSFP and proposes several projection and contraction algorithms to solve the multiple-sets split feasibility problem and gives proof of convergence. Chapter five carrys out numerical experiments and makes some analysis about the experimental results.