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应用数学学报  2012, Vol. Issue (4): 719-727    DOI:
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Stiefel流形上的梯度下降法
吴秋峰, 刘振忠
东北农业大学理学院, 哈尔滨 150030
Gradient Descent on the Stiefel Manifold
Wu Qiufeng, Liu Zhenzhong
College of Science, Northeast Agricultural University, Harbin 150030
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摘要 基于Stiefel 流形上算法的几何框架, 本文提出了Stiefel流形上的梯度下降法. 理论上给出了算法收敛性定理. 三个数值仿真算例表明算法是有效的, 与其他方法相比具有更快的收敛速度.
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吴秋峰
刘振忠
关键词约束非线性优化问题   梯度下降法   Stiefel流形     
Abstract: This paper presents gradient descent on the Stiefel manifolds based on algorithmic geometrical framework on the Stiefel manifolds. Theoretically, convergence theorem of this algorithm is given. Three numerical simulations are shown to verify the efficiency of the proposed algorithm, and to have faster convergence rate compared with other methods.
Key wordsconstrained nonlinear optimization problem   gradient descent   Stiefel manifold   
收稿日期: 2011-07-09;
基金资助:东北农业大学科学技术资助项目(2011RCA01).
通讯作者: 刘振忠     E-mail: lzz00@126.com
引用本文:   
吴秋峰,刘振忠. Stiefel流形上的梯度下降法[J]. 应用数学学报, 2012, (4): 719-727.
Wu Qiufeng,Liu Zhenzhong. Gradient Descent on the Stiefel Manifold[J]. Acta Mathematicae Applicatae Sinica, 2012, (4): 719-727.
 
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