A new halfspace-relaxation projection method for the split feasibility problem

Let C and Q be nonempty closed convex sets in Rn and Rm, respectively, and A an m by n real matrix. The problem, to find x∈C with Ax∈Q if such x exist, is called the split feasibility problem (SFP). This problem is important in intensity-modulated radiation therapy, signal processing, image reconstruction and so on. In this paper, based on a new reformulation for the SFP, we propose a new halfspace-relaxation projection method for the SFP. The method is implemented very easily and is proven to be fully convergent to the solution for the case where the solution set of the SFP is nonempty. Preliminary computational experience is also reported.