A simple projection method for solving the multiple-sets split feasibility problem

In this article, we first introduce a simple but practical projection method for solving the multiple-sets split feasibility problem, which is to find a point in the intersection of a family of closed convex sets in one space, such that its image under a linear transformation is in the intersection of another family of closed convex sets in the image space. In each iteration of this method, the step-size is directly computed, and is shown to be the best for the current direction. Then we consider the corresponding relaxed projection scheme for the proposed method. The theoretical convergence results are established. Preliminary numerical experiments show that this simple method and its relaxed scheme are easy to implement and practical.