ACCELERATED OPTIMIZATION WITH ORTHOGONALITY CONSTRAINTS  

作　　者：Jonathan W.Siegel 

机构地区：[1]Department of Mathematics,Pennsylvania State University,University Park,PA,USA

出　　处：《Journal of Computational Mathematics》2021年第2期207-226,共20页计算数学（英文）

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.

关 键 词：Riemannian optimization Stiefel manifold Accelerated gradient descent Eigenvector problems Electronic structure calculations 

分 类 号：O22[理学—运筹学与控制论]