求解多集分裂可行问题的一种新的松弛投影算法

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求解多集分裂可行问题的一种新的松弛投影算法张艳君^1,2, 赵金玲¹, 徐尔¹1. 北京科技大学数理学院, 北京 100083;
2. 北京科技大学天津学院, 天津 301800 A New Relaxed Projection Method to Solve the Multiple-sets Split Feasibility Problem ZHANG Yanjun^1,2, ZHAO Jinling¹, XU Er¹1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
2. Tianjin College, University of Science and Technology Beijing, Tianjin 301800, China

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摘要本文提出了求解多集分裂可行问题（Multiple-sets Split Feasibility Problem，简称MSFP）的一种新的松弛投影算法.已有求解MSFP的算法大多采用邻近函数p（x）：=（1/2

α_i||x-P_{C_i}（x）||²+（1/2

λ_j||Ax-P_{Q_j}（Ax）||²度量点到所有集合的距离并在迭代中直接利用其梯度方向，与此不同，本文引入了新的搜索方向，并基于此提出了新的算法.搜索方向的不同导致了算法的收敛性证明上的明显差异.初步的数值计算结果表明新算法对于不同的问题都能够有较快的收敛速度，且在问题维数增大时表现得越发明显.

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收稿日期: 2013-11-11

PACS:	O221.2
	O242.2

基金资助:国家自然科学基金（11101028，11271206），北京市青年英才计划资助项目.

引用本文:

张艳君, 赵金玲, 徐尔. 求解多集分裂可行问题的一种新的松弛投影算法[J]. 应用数学学报, 2017, 40(5): 641-652. ZHANG Yanjun, ZHAO Jinling, XU Er. A New Relaxed Projection Method to Solve the Multiple-sets Split Feasibility Problem. Acta Mathematicae Applicatae Sinica, 2017, 40(5): 641-652.

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