点击次数：

影响因子：4.3

DOI码：10.1002/nla.2561

发表刊物：Numerical Linear Algebra with Applications

关键字：block Krylov subspace, block Lanczos method, hard case, trust-region subproblem

摘要：The trust-region subproblem (TRS) plays a vital role in numerical optimization, numerical linear algebra, and many other applications. It is known that the TRS may have multiple optimal solutions in the hard case. In [Carmon and Duchi, SIAM Rev., 62 (2020), pp. 395–436], a block Lanczos method was proposed to solve the TRS in the hard case, and the convergence of the optimal objective value was established. However, the convergence of the KKT error as well as that of the approximate solution are still unknown for this method. In this paper, we give a more detailed convergence analysis on the block Lanczos method for the TRS in the hard case. First, we improve the convergence speed of the approximate objective value. Second, we derive the speed of the KKT error tends to zero.Third, we establish the convergence of the approximation solution, and show theoretically that the projected TRS obtained from the block Lanczos method will be close to the hard case more and more as the block Lanczos process proceeds. Numerical experiments illustrate the effectiveness of our theoretical results.

备注：中科院 2 区

第一作者：Bo Feng; Gang Wu

论文类型：SCI

通讯作者：Gang Wu

论文编号：e2561

学科门类：理学

一级学科：数学

文献类型：SCI

是否译文：否

发表时间：2024-04-25

收录刊物：SCI

发布期刊链接：https://doi.org/10.1002/nla.2561