Split feasibility problem (SFP) is to find a point which belongs to one convex set in one space, such that its image under a linear transformation belongs to another convex set in the image space. This paper deals with a unified regularized SFP for the convex case. We first construct a self-adaptive regularization iterative algorithm by using Armijo-like search for the SFP and show it converges at a subliner rate of $ O(1/k) $, where $ k $ represents the number of iterations. More interestingly, inspired by the acceleration technique introduced by Nesterov[12], we present a fast Armijo-like regularization iterative algorithm and show it converges at rate of $ O(1/k^{2}) $. The efficiency of the algorithms is demonstrated by some random data and image debluring problems.

中文翻译：

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解决分裂可行性问题的快速自适应正则化迭代算法

分裂可行性问题（SFP）是在一个空间中找到一个属于一个凸集的点，从而使其在线性变换下的图像在图像空间中属于另一个凸集。本文针对凸情况处理统一的正则化SFP。我们首先使用类Armijo搜索SFP来构造自适应正则化迭代算法，并显示它以$ O（1 / k）$的子线性速率收敛，其中$ k $表示迭代次数。更有趣的是，受Nesterov引入的加速技术的启发[12]，我们提出了一种快速的类似Armijo的正则化迭代算法，并证明它以$ O（1 / k ^ {2}）$的速率收敛。一些随机数据和图像模糊问题证明了算法的有效性。