报告题目 (Title)：A regularizing multilevel approach for nonlinear inverse problems（非线性反问题的一种正则化多层次方法）
报告人 (Speaker)： 王薇 教授（嘉兴大学）
报告时间 (Time)：2025年3月13日(周四) 19:00
报告地点 (Place)：腾讯会议(516 391 552)
邀请人(Inviter)：朱佩成 教授
主办部门：理学院数学系
报告摘要：In this talk, we propose a multilevel method for solving nonlinear ill-posed problems F(x) = y in Banach spaces. By minimizing the discretized version of the regularized functionals for different discretization levels, we define a sequence of regularized approximations to the exact solution, which is shown to be stable and globally convergent for arbitrary initial guesses. The penalty terms $\Theta$ in regularized functionals are allowed to be non-smooth to include $L^p-L^1$ or $L^p-$TV (total variation) cases, which are important in reconstructing special features of solutions such as sparsity and discontinuities. Two parameter identification examples are presented to validate the theoretical analysis and verify the method's effectiveness.
