An accelerated Kaczmarz type method for nonlinear inverse problems in Banach spaces with uniformly convex penalty

DOI10.1016/j.cam.2020.113211zbMath1456.65146OpenAlexW3091259097MaRDI QIDQ2222156

Yanyan Li

Publication date: 3 February 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2020.113211

zbMATH Keywords

Banach spacesiterative regularizationnonlinear inverse problemsKaczmarz type methoduniformly convex penalty

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical computation of solutions to systems of equations (65H10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (4)

A data-driven Kaczmarz iterative regularization method with non-smooth constraints for ill-posed problems ⋮ A Hadamard fractional total variation-Gaussian (HFTG) prior for Bayesian inverse problems ⋮ Levenberg-Marquardt method with general convex penalty for nonlinear inverse problems ⋮ An accelerated homotopy-perturbation-Kaczmarz method for solving nonlinear inverse problems

Uses Software

• KELLEY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Regularization methods in Banach spaces.
• Convergence analysis of the homotopy perturbation method for solving nonlinear ill-posed operator equations
• Nonsmooth analysis
• Iterative regularization methods for nonlinear ill-posed problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• An iteration regularization method with general convex penalty for nonlinear inverse problems in Banach spaces
• Kaczmarz methods for regularizing nonlinear ill-posed equations. I: Convergence analysis
• On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations
• Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
• An iterative regularization method for nonlinear problems based on Bregman projections
• Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals
• Iterative regularization with a general penalty term—theory and application to L ¹ and TV regularization
• Inexact Newton--Landweber Iteration in Banach Spaces with NonSmooth Convex Penalty Terms
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation
• Accelerated Landweber iteration in Banach spaces
• Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems
• Sparsity regularization for parameter identification problems
• Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces
• Fast subspace optimization method for nonlinear inverse problems in Banach spaces with uniformly convex penalty terms
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
• Regularizing Newton--Kaczmarz Methods for Nonlinear Ill-Posed Problems

This page was built for publication: An accelerated Kaczmarz type method for nonlinear inverse problems in Banach spaces with uniformly convex penalty