Speaker: Prof. Gang Wu（吴钢教授）

Time: 11:30-12:30, 15 February 2023 (Wednesday) (Beijing time)

Venue: A103, Lijiao Building

Tencent Meeting ID: 815-235-194

Abstract

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 the condition numbers of them. 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 TRS problem beforehand.

About Prof. Wu

吴钢，博士、中国矿业大学数学学院教授、博士生导师；江苏省“333 工程” 中青年科学技术带头人，江苏省“青蓝工程”中青年学术带头人，现任江苏省计算数学学会副理事长。主要研究方向：数值代数、机器学习与数据挖掘、大规模科学与工程计算等。先后主持国家自然科学基金项目、江苏省省自然科学基金项目多项，在国际知名杂志，如：SIAM Journal on Numerical Analysis, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, IEEE Transactions on Knowledge and Data Engineering, Pattern Recognition, Machine Learning, ACM Transactions on Information Systems 等期刊发表学术论文多篇