A Relaxed CQ Algorithm for Solving Split Feasibility Problem

The split feasibility problem(SFP) is to find a point x ∈ C such that Ax ∈ Q, where A, H/sub 1/ → H/sub 2/ is a bounded linear operator, and C and Q be nonempty closed convex subset of Hilbert space H/sub 1/ and H/sub 2/, respectively. In this paper, we proposed a relaxed CQ algorithm for solving split feasibility problem. The iterative algorithm generates a sequence fxng as follows x/sub n+1/=(1- α /sub n/)x/sub n/+ α /sub n/Pc/sub n/(x/sub n/- γ A*(I-P/sub Qn)Ax/sub n/), n ≥ 0, where 0 < γ < 2/A/sup 2/, x/sub 0/ ∈ H/sub 1/, P/sub Cn/ and P/sub Qn/ are the nearest point projections onto C/sub n/ and Q/sub n/, respectively. Then we proved that CQ algorithm converges weakly to a solution of the SFP.