The split feasibility problem is to find a point x^∗ with the property that x^∗∈ C and Ax^∗∈ Q, where C and Q are nonempty closed convex subsets of real Hilbert spaces X and Y, respectively, and A is a bounded linear operator from X to Y. The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity-modulated radiation therapy. In this paper, we introduce a new inertial relaxed CQ algorithm for solving the split feasibility problem in real Hilbert spaces and establish weak convergence of the proposed CQ algorithm under certain mild conditions. Our result is a significant improvement of the recent results related to the split feasibility problem.

分割可行性问题是要找到一个点X ^*与该属性X ^* ∈ Ç和甲X ^* ∈ Q，其中Ç和Q是实Hilbert空间的非空闭凸子集X和ÿ，分别和阿是有界从X到Y的线性算子。分裂可行性问题模拟了由相位恢复问题和强度调制放射疗法引起的逆问题。在本文中，我们介绍了一种新的惯性松弛CQ算法解决实际Hilbert空间中的分裂可行性问题，并在一定的温和条件下建立了所提出的CQ算法的弱收敛性。我们的结果是与拆分可行性问题相关的最新结果的重大改进。