Iterative regularization for constrained minimization formulations of nonlinear inverse problems

Barbara Kaltenbacher () and Kha Huynh ()
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Barbara Kaltenbacher: Alpen-Adria-Universität Klagenfurt
Kha Huynh: Alpen-Adria-Universität Klagenfurt

Computational Optimization and Applications, 2022, vol. 81, issue 2, No 8, 569-611

Abstract: Abstract In this paper we study the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type methods. We carry out a convergence analysis in the sense of regularization methods and discuss applicability to the problem of identifying the spatially varying diffusivity in an elliptic PDE from different sets of observations. Among these is a novel hybrid imaging technology known as impedance acoustic tomography, for which we provide numerical experiments.

Keywords: Inverse problems; Iterative regularization; Coefficient identification in elliptic PDEs; Impedance acoustic tomography (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-021-00343-x

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