Inexact Newton--Landweber Iteration in Banach Spaces with NonSmooth Convex Penalty Terms

DOI10.1137/130940505zbMath1326.65064OpenAlexW1830298384MaRDI QIDQ3196609

Qi-nian Jin

Publication date: 30 October 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/b2f87c50ddcac6cb2f855ce83fbffe88beb7b7d3

zbMATH Keywords

convergenceBanach spacediscrepancy principlenumerical simulationnonlinear inverse problemsBregman distanceuniformly convex functionsinexact Newton-Landweber iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (11)

REGINN-IT method with general convex penalty terms for nonlinear inverse problems ⋮ Convergence analysis of inexact Newton–Landweber iteration under Hölder stability ⋮ An asymptotical regularization with convex constraints for inverse problems ⋮ Generalized inexact Newton regularization for nonlinear ill-posed problems in Banach spaces ⋮ Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems ⋮ Hanke-Raus rule for Landweber iteration in Banach spaces ⋮ Deep unfolding as iterative regularization for imaging inverse problems ⋮ An accelerated Kaczmarz type method for nonlinear inverse problems in Banach spaces with uniformly convex penalty ⋮ Inexact Newton regularization in Banach spaces based on two-point gradient method with uniformly convex penalty terms ⋮ Bouligand-Levenberg-Marquardt iteration for a non-smooth ill-posed inverse problem ⋮ Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems ^*

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