报告人：吴钢（中国矿业大学）

时间：2022年11月12日 15:00-

腾讯会议ID：482 139 856

摘要：The generalized Lanczos trust-region (GLTR) method is one of the most popular approaches for solving large-scale trust-region subproblem (TRS). Recently, Jia and Wang [Z. Jia and F. Wang, SIAM J. Optim., 31 (2021), pp. 887--914] considered the convergence of this method and established some a prior error bounds on the residual, the solution and the Largrange multiplier. In this paper, we revisit the convergence of the GLTR method and try to improve these bounds. First, we establish a sharper upper bound on the residual. Second, we give a new bound on the distance between the approximation and the exact solution, and show that the convergence of the approximation has nothing to do with the associated spectral separation. Third, we present some non-asymptotic bounds for the convergence of the Largrange multiplier, and define a factor that plays an important role on the convergence of the Largrange multiplier. Numerical experiments demonstrate the effectiveness of our theoretical results.

简介：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：大规模科学与工程计算、数值代数、机器学习与数据挖掘等。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 Matrix Analysis and Applications, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, Pattern Recognition, Machine Learning等期刊发表学术论文多篇。

邀请人：李寒宇