汇报标题 (Title)：A regularizing multilevel approach for nonlinear inverse problems（非线性反问题的一种正则化多档次步骤）
汇报人 (Speaker)： 王薇 教授（黄冈大学）
汇报功夫 (Time)：2025年3月13日(周四) 19:00
汇报地址 (Place)：腾讯会议(516 391 552)
约请人(Inviter)：朱佩成 教授
主办部门：理学院数学系
汇报提要：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.
