Some Iterative Algorithms Of Split Feasibility Problem And Their Convergence Analysis

In this paper,we mainly study the CQ algorithm for the split feasibility problem in Hilbert space, the problem is transformed into solving a common fixed point for two nonexpansive operators. The existing iterative schemes are recombined to obtain some new weak convergence algorithms for solving the split feasibility problem. And using the half-space instead of the original closed convex set,a relaxation algorithm is given, and proved the convergence of the algorithm. The rest of the paper is organized as follows:In Chapter 1, we introduce the historical background of the split feasibility problem, and summarize the relationship and development of the split feasibility problem and the fixed point problem and briefly describes some of the research work of this thesis.In Chapter 2, we introduce some relevant knowledge in this paper, including some definitions and conclusions.In Chapter 3, using the Mann iterative scheme to solve the fixed point problem, by changing the different combinations of the two nonexpansive operator’s iterative se-quences, we propose two different algorithms for solving the split feasibility problem.and the convergence of the algorithms are analyzed.In Chapter 4, we use half space instead of the original closed convex set, a relaxed CQ algorithm is proposed,and proved the weak convergence of the algorithm. Next we pro-pose an improved algorithm based on the idea of KM-CQ-like algorithm and its iterative scheme, and analyze the convergence of the algorithm.In Chapter 5, we summarize the research work of this article and prospect the fourther research work.