Algorithm Study For A Kind Of The Variational Inequality Problem And The Split Feasibility Problem

In this thesis,we mainly consider the projection algorithms for solving the variational inequality with fixed point constraints and the split feasibility problem. It contains three chapters.Chapter 1 mianly discusses the current development of the discussed issue, i.e.the variational inequality problem,fixed points of a nonexpansive mapping problem,and the problem of finding the common element of two problems,the split feasibility problem.The main contribution and work of this paper is also listed in this chapter at last.In chapter 2,we consider projection algorithms for the problem of the common elements of the variational inequality problem and fixed points problem of a nonexpansive mapping problem.We first translate this problem to another problem which can be solved by contraction projection algorithm.The algorithm has two improvement:(1) mapping A is consecutive and pseudomonotone,weaken the assumptions furthermore;(2) Compressed projection's region,it can be guaranteed that the next iteration point is closer to the solution set of questions in theory.At last we prove the global convergence of the algorithm and R-linear convergent rate.For the split feasibility problem(SPF),we first analyze the algorithms given by Byrne,Yang and Qu for this problem in Chapter 3.Then,we propose a modified relaxed CQ projection method for solving the split feasibility problem based on the method proposed by Qu,i.e.the fixed step relaxed CQ aigorithm.For the new algorithm,we use a fixed step size saving the time of searching the step,and we aslo prove the global convergence of the algorithm.The given preliminary computational experiments show that this method is promising. Variational inequality problem;fixed point;projection operator;pseduo-monotone mapping;nonexpansive mapping;split feasibility problem;global convergence; R-linear convergent rate.