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

Let C and Q be nonempty closed convex sets in image and image, respectively, and A an m by n real matrix. The problem, to find xset membership, variantC with Axset membership, variantQ 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.