| 多集分裂等式问题的逐次松弛投影算法 |
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| 引用本文： | 周雪玲,李梅霞,车海涛.多集分裂等式问题的逐次松弛投影算法[J].运筹学学报,2021,25(2):93-103. |
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| 作者姓名： | 周雪玲 李梅霞 车海涛 |
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| 作者单位： | 1. 扬州大学数学科学学院, 江苏扬州 225002;2. 潍坊学院数学与信息科学学院, 山东潍坊 261061 |
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| 基金项目： | 国家自然科学基金(11401438);国家自然科学基金(11571120);山东省自然科学基金(ZR2020MA027);山东省自然科学基金(ZR2019MA022) |
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| 摘 要： | 多集分裂等式问题是分裂可行性问题的拓展问题，在图像重建、语言处理、地震探测等实际问题中具有广泛的应用。为了解决这个问题，提出了逐次松弛投影算法，设计了变化的步长，使其充分利用当前迭代点的信息且不需要算子范数的计算，证明了算法的弱收敛性。数值算例验证了算法在迭代次数与运行时间等方面的优越性。
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| 关 键 词： | 多集分裂等式问题 逐次松弛投影算法 收敛性 |
| 收稿时间： | 2019-10-08 |
Successive relaxed projection algorithm for multiple-sets split equality problem |
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| Xueling ZHOU,Meixia LI,Haitao CHE.Successive relaxed projection algorithm for multiple-sets split equality problem[J].OR Transactions,2021,25(2):93-103. |
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| Authors: | Xueling ZHOU Meixia LI Haitao CHE |
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| Institution: | 1. School of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China;2. School of Mathematics and Information Science, Weifang University, Weifang 261061, Shandong, China |
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| Abstract: | The multiple-sets split equality problem is an extended split feasibility problem, which has a wide application in image reconstruction, language processing, and seismic exploration. In order to solve this problem, we propose a successive relaxed projection algorithm with a variable stepsize which can fully use the information of the current iteration point and does not need the calculation of the operator norm. Furthermore the weak convergence of the algorithm is proved. The numerical examples show the superiority of the algorithm in the number of iterations and the running time. |
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| Keywords: | multiple-sets split equality problem successive relaxed projection algorithm convergence |
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