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影响因子：2.1

DOI码：10.1093/imanum/drae042

发表刊物：IMA Journal of Numerical Analysis

关键字：Trust-region subproblem (TRS), Perturbation analysis, Condition number, First-order perturbation, Easy case, Nearly hard case

摘要：Trust-region subproblem (TRS) is an important problem arising in many applications such as numerical optimization, Tikhonov regularization of ill-posed problems, and constrained eigenvalue problems. In recent decades, extensive works focus on how to solve the trust-region subproblem efficiently. To the best of our knowledge, there are few results on perturbation analysis of the trust-region subproblem. In order to fill in this gap, we focus on first-order perturbation theory of the trust-region subproblem. The main contributions of this paper are three-fold. First, suppose that the TRS is in easy case, we give a sufficient condition under which the perturbed TRS is still in easy case. Second, with the help of the structure of the TRS and the classical eigenproblem perturbation theory, we perform first-order perturbation analysis on the Lagrange multiplier and the solution of the TRS, and define their condition numbers. Third, we point out that the solution and the Lagrange multiplier could be well-conditioned even if TRS is in nearly hard case. The established results are computable, and are helpful to evaluate ill-conditioning of the large-scale TRS problem beforehand. Numerical experiments show the sharpness of the established bounds and the effectiveness of the proposed strategies.

备注：接收； SCI 2区

第一作者：Bo Feng; Gang Wu

论文类型：SCI

通讯作者：Gang Wu

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：2024-05-07

收录刊物：SCI

发布期刊链接：https://doi.org/10.1093/imanum/drae042