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, H₁ → H₂ is a bounded linear operator, and C and Q be nonempty closed convex subset of Hilbert space H₁ and H₂, respectively. In this paper, we proposed a relaxed CQ algorithm for solving split feasibility problem. The iterative algorithm generates a sequence {x_n} as follows x_n+1=(1-α_n)x_n/+ α_nPc_n(x_n-γ A*(I-PQ_n)Ax_n), n ≥ 0, where 0 <; γ <; 2/||A||², x₀ ∈ H₁, PC_n and PQ_n are the nearest point projections onto C_n and Q_n, respectively. Then we proved that CQ algorithm converges weakly to a solution of the SFP.