| 超平面交单调锥上投影算子的快速算法及其实现 |
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| 引用本文： | 刘勇进,汤婉红.超平面交单调锥上投影算子的快速算法及其实现[J].福州大学学报(自然科学版),2023,51(3):293-300. |
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| 作者姓名： | 刘勇进 汤婉红 |
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| 作者单位： | 福州大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 摘 要： | 研究超平面交单调锥上的投影问题，给出求解该问题的池相邻违反算法和半光滑牛顿法，并对算法进行有效性分析，最后将两种算法进行数值对比.数值实验结果表明：在求解随机数据集上的投影问题时，池相邻违反算法比目前流行的半光滑牛顿算法更高效.
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| 关 键 词： | 超平面交单调锥 池相邻违反算法 半光滑牛顿法 投影算子 |
| 收稿时间： | 2022/11/25 0:00:00 |
| 修稿时间： | 2022/12/26 0:00:00 |
Fast algorithms for computing the projection operator onto the intersection of a hyperplane and monotonic cone and their implementations |
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| LIU Yongjin,TANG Wanhong.Fast algorithms for computing the projection operator onto the intersection of a hyperplane and monotonic cone and their implementations[J].Journal of Fuzhou University(Natural Science Edition),2023,51(3):293-300. |
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| Authors: | LIU Yongjin TANG Wanhong |
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| Institution: | School of Mathematics and Statistics |
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| Abstract: | This paper studies the projection operator onto the intersection of a hyperplane and monotonic cone. The PAV algorithm and semi-smooth Newton algorithm for solving this problem are given, and the effectiveness of the algorithms is analyzed. Finally, the two algorithms are numerically compared and numerical experiments are carried out. The results show that the PAV algorithm is more efficient than the currently popular semi-smooth Newton algorithm in solving the projection problem on random data sets. |
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| Keywords: | intersection of a hyperplane and monotonic cone PAV algorithm semi-smooth Newton algorithm projection operator |
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