A successive centralized circumcentered-reflection method for the convex feasibility problem
A successive centralized circumcentered-reflection method for the convex feasibility problem
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DOI：
10.1007/s10589-023-00516-w
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发表时间：
2022-12
影响因子：
2.2
通讯作者：
R. Behling;Yunier Bello-Cruz;A. Iusem;Di Liu;L. Santos
中科院分区：
文献类型：
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作者：
R. Behling;Yunier Bello-Cruz;A. Iusem;Di Liu;L. Santos
本文给出了求解欧氏空间中凸可行性问题的具有多个控制序列的圆心反射法的逐次集中过程。在假设一个标准误差界成立的情况下，我们证明了最多违反约束控制序列的方法的线性收敛。此外，在目标集上附加光滑性的假设下，我们建立了超线性收敛。数值实验证实了该方法的有效性。
In this paper, we present a successive centralization process for the circumcentered-reflection method with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove the linear convergence of the method with the most violated constraint control sequence. Moreover, under additional smoothness assumptions on the target sets, we establish the superlinear convergence. Numerical experiments confirm the efficiency of our method.