Regularization Based on All-At-Once Formulations for Inverse Problems

DOI10.1137/16M1060984zbMath1347.65104arXiv1603.05332MaRDI QIDQ2817783

Barbara Kaltenbacher

Publication date: 2 September 2016

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

Full work available at URL: https://arxiv.org/abs/1603.05332

zbMATH Keywords

convergenceregularizationinverse problemsparameter identificationnumerical comparisonTikhonov methodall-at-once formulations

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (14)

Discretization of parameter identification in PDEs using neural networks ⋮ The domain derivative for semilinear elliptic inverse obstacle problems ⋮ Regularization of inverse problems via box constrained minimization ⋮ Learning-informed parameter identification in nonlinear time-dependent PDEs ⋮ The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition ⋮ Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case ⋮ Minimization Based Formulations of Inverse Problems and Their Regularization ⋮ On iteratively regularized predictor–corrector algorithm for parameter identification ^* ⋮ Some application examples of minimization based formulations of inverse problems and their regularization ⋮ The Tangential Cone Condition for Some Coefficient Identification Model Problems in Parabolic PDEs ⋮ Parameter Identification for the Landau–Lifshitz–Gilbert Equation in Magnetic Particle Imaging ⋮ A penalty-free approach to PDE constrained optimization: application to an inverse wave problem ⋮ A model reference adaptive system approach for nonlinear online parameter identification ⋮ Iterative regularization for constrained minimization formulations of nonlinear inverse problems

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