| 梅 奎，欧阳薇*.求解凸可行性问题的循环平均交替反射法[J].海南师范大学学报自科版,2022,35(3):268-274 |
| 求解凸可行性问题的循环平均交替反射法 |
| Cyclic Average Alternating Reflection Method for Solving ConvexFeasibility Problems |
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| DOI：10.12051/j.issn.1674-4942.2022.03.005 |
| 中文关键词: 凸可行性问题 均值算子 不动点 Douglas-Rachford算法 |
| 英文关键词: convex feasibility problem averaged operator fixed point Douglas-Rachford algorithm |
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| 中文摘要: |
| Douglas-Rachford 算法是一种可用于解决可行性问题的优化方法。循环 DouglasRachford 算法和松弛平均交替反射算法也被成功地应用于求解多个闭凸集的可行性问题。本文引
入一种基于松弛平均交替反射法和循环 Douglas-Rachford 算法的新算法，并利用均值算子和不动
点的性质证明了该算法的收敛性。该算法可以直接用于求解希尔伯特空间中多个集合的凸可行
性问题。 |
| 英文摘要: |
| :Douglas-rachford algorithm is an optimization method which can be used to solve feasibility problems.The cy⁃
clic Douglas-Rachford algorithm and the relaxed averaged alternating reflection algorithm have been successfully applied
to feasibility problems with multiple closed convex sets. In this paper, a new algorithm is proposed based on relaxed aver⁃
aged alternating reflection method and cyclic Douglas-Rachford algorithm, and the convergence of such algorithm is proved
by utilizing the properties of averaged operator and fixed point. This algorithm can be directly applied to solve convex feasi⁃
bility problems with multiple sets in Hilbert Spaces. |
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