ACCELERATED OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS

• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 207-226
• 页数: 20页
• 语种: 英文
• DOI: 10.4208/jcm.1911-m2018-0242

摘要

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints.To demonstrate the effectiveness of our method,we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number,and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold.Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large,ill-conditioned problems.