Generalized Inexact Newton-Landweber Iteration for Possibly Non-Smooth Inverse Problems in Banach Spaces

Ruixue Gu, Hongsun Fu () and Zhuoyue Wang
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Ruixue Gu: School of Science, Dalian Maritime University, Dalian 116026, China
Hongsun Fu: School of Science, Dalian Maritime University, Dalian 116026, China
Zhuoyue Wang: School of Science, Dalian Maritime University, Dalian 116026, China

Mathematics, 2023, vol. 11, issue 7, 1-20

Abstract: In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth convex penalty terms, including L 1 -like and total variation-like penalty functionals, to capture special features of solutions such as sparsity and piecewise constancy. Furthermore, the inaccurate inner solver is incorporated into the minimization problem in each iteration step. Under some assumptions, based on ε -subdifferential, we establish the convergence analysis of the proposed method. Finally, some numerical simulations are provided to illustrate the effectiveness of the method for solving both smooth and non-smooth nonlinear inverse problems.

Keywords: nonlinear inverse problems; non-smooth forward mappings; inexact Newton regularization; non-smooth convex penalty; Landweber iteration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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