Lavrentiev's regularization method in Hilbert spaces revisited

DOI10.3934/ipi.2016019zbMath1348.65091arXiv1506.01803OpenAlexW2962717399MaRDI QIDQ326413

Bernd Hofmann, Barbara Kaltenbacher, Elena Resmerita

Publication date: 12 October 2016

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01803

zbMATH Keywords

convergence analysismonotone operatorssource conditionsregularization parameter choiceLavrentiev regularization

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Inverse problems for PDEs (35R30) Inverse problems for integral equations (45Q05) Numerical solution to inverse problems in abstract spaces (65J22)

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Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces ⋮ Shape derivative for penalty-constrained nonsmooth-nonconvex optimization: cohesive crack problem ⋮ A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition ⋮ Converse Results, Saturation and Quasi-optimality for Lavrentiev Regularization of Accretive Problems ⋮ Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations ⋮ Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space ⋮ Optimal rates for Lavrentiev regularization with adjoint source conditions ⋮ Third-order derivative-free methods in Banach spaces for nonlinear ill-posed equations ⋮ A Regularization Approach for an Inverse Source Problem in Elliptic Systems from Single Cauchy Data ⋮ Derivative free regularization method for nonlinear ill-posed equations in Hilbert scales ⋮ A regularized variational inequality approach for nonlinear monotone ill-posed equations ⋮ Newton-Kantorovich regularization method for nonlinear ill-posed equations involving \(m\)-accretive operators in Banach spaces ⋮ Direct regularization for system of integral-algebraic equations of index-1

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