点击次数：

影响因子：3.1

DOI码：10.1137/23M1568545

发表刊物：SIAM Journal on Scientific Computing

关键字：quadratic minimization problems with orthogonality constraints, QMPO, block Lanczos, block Krylov subspace

摘要：Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale QMPO. Krylov subspace methods are popular for large-scale optimization problems. In this work, we propose a block Lanczos method for solving the large-scale QMPO. In the proposed method, the original problem is projected into a small-sized one, and the Riemannian trust-region method is employed to solve the reduced QMPO. Convergence results on the optimal solution, the optimal objective function value, the multiplier, and the KKT error are established. Moreover, we give the convergence speed of the approximate solution and show that if the block Lanczos process terminates, then an exact KKT solution is derived. Numerical experiments illustrate the numerical behavior of the proposed algorithm and demonstrate that it is more powerful than many state-of-the-art algorithms for large-scale QMPO.

第一作者：Bo Feng; Gang Wu

论文类型：SCI二区TOP

通讯作者：Gang Wu

学科门类：理学

一级学科：数学

文献类型：SCI

卷号：46

期号：2

页面范围：A884-A905

是否译文：否

发表时间：2024-03-08

收录刊物：SCI

发布期刊链接：https://epubs.siam.org/doi/10.1137/23M1568545