Parameter identification in PDEs by the solution of monotone inclusion problems
Numerical Analysis
2025-02-26 v2 Numerical Analysis
Analysis of PDEs
Optimization and Control
Abstract
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method.
Cite
@article{arxiv.2403.04557,
title = {Parameter identification in PDEs by the solution of monotone inclusion problems},
author = {Pankaj Gautam and Markus Grasmair},
journal= {arXiv preprint arXiv:2403.04557},
year = {2025}
}