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.
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机译：分裂可行性问题（SFP）是找到一个点x∈C，使得Ax∈Q，其中A，H / sub 1 /→H / sub 2 /是有界线性算子，而C和Q是非空闭合凸子集希尔伯特空间分别为H / sub 1 /和H / sub 2 /。在本文中，我们提出了一种松弛的CQ算法来解决分裂可行性问题。迭代算法生成序列fxng如下x / sub n + 1 / =（1-α/ sub n /）x / sub n / +α/ sub n / Pc / sub n /（x / sub n /-γ A *（IP / sub Qn）Ax / sub n /），n≥0，其中0 <γ<2 / A / sup 2 /，x / sub 0 /∈H / sub 1 /，P / sub Cn /和P / sub Qn /是分别在C / sub n /和Q / sub n /上的最近点投影。然后我们证明了CQ算法弱收敛到SFP的解。
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