| 求解多集分裂可行问题的一种共轭梯度法 |
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| 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共轭梯度法[J]. 数值计算与计算机应用, 2013, 0(4): 249-256 |
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| 作者姓名： | 张艳君 赵金玲 徐尔 |
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| 作者单位： | 北京科技大学数理学院,北京100083 |
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| 基金项目： | 基金项目：国家自然科学基金青年基金项目资助（11101028）,中央高校基本科研业务费资助（FRF-BR-11-001A）. |
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| 摘 要： | 基于求解多集分裂可行问题与非线性最优化问题的等价性，考虑Jinling Zhao and Qingzhi Yang在[1]中提出的求解SFP的共轭梯度法和Censor等在[2]中提出的梯度投影法，尝试运用共轭梯度法求解多集分裂可行问题；并且证明了所构造算法的收敛性．提出的新算法克NT求矩阵逆的缺点．初步的数值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，具有良好的稳定性和可行性，在问题维数增大时表现得越发明显．
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| 关 键 词： | 多集分裂可行问题 共轭梯度法 Lipschitz连续 正交投影 |
A CONJUGATE GRADIENT ALGORITHM FOR SOLVING THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM |
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| Zhang Yanjun Zhao Jinling Xu Er. A CONJUGATE GRADIENT ALGORITHM FOR SOLVING THE MULTIPLE-SETS SPLIT FEASIBILITY PROBLEM[J]. Journal on Numerical Methods and Computer Applications, 2013, 0(4): 249-256 |
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| Authors: | Zhang Yanjun Zhao Jinling Xu Er |
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| Affiliation: | Zhang Yanjun Zhao Jinling Xu Er (University of Science and Technology Beijing, School of Mathematics and Physics, Beijing 100083, China) |
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| Abstract: | Based on the equivalence of the multiple-sets split feasibility problem and an optimiza- tion problem, considering the conjugate gradient method that Jinling Zhao and Qingzhi Yang presented in [1] for solving the SFP and the gradient projection method which was proposed by Censor et al in [2]. We use a conjugate gradient method for solving the multiple-sets split feasibility problem and prove the convergence of the new algorithm. The new algorithm does not need to calculate inverse of matrix. In the preliminary numerical experiments the new algorithm has shown faster convergence rate. It has favorable feasibility and stability for a variety of problems. |
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| Keywords: | multiple-sets split feasibility problem conjugate gradient method Lipschitz- continuous orthogonal projection |
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