The Applications Of Alternating Projections Method

The constraint optimization problems are a class of important optimization problems. In 1930, John Von Neumann first proposed the alternating projection algorithm, which is a simple and practical approach to solve these problems.This paper consists of three chapters. My main work is in the last two chapters.In the second chapter of this paper, we first analyse the alternating projection algorithm convergence rate based on the work of predecessors; then in the next section, we give the applications of alternating projection algorithm: it is not only one of the effective ways to solve large-scale system of linear equations, but also can effectively find a feasible point of the line programming problems. At the same time, it can be extended to find a feasible point of the semidefinite programming problems. Finally, in the second chapter we give the numerical experiments, which show that the alternating projection algorithm is effective for solving the above mentioned problems.The third chapter of this paper is relatively independent of the other chapters, and it mainly studies the property of variational inequality's solution set. We give a new proof for the property of linear variational inequality's solution set, and the new proof seems simpler than the original one.