255. Parameter identification in PDEs by the solution of monotone inclusion problems
Invited abstract in session FD-3: Variational techniques in optimization, stream Variational analysis: theory and algorithms.
Friday, 14:10 - 15:50Room: M:J
Authors (first author is the speaker)
| 1. | Pankaj Gautam
|
| Applied Mathematics and Scientific Computing, Indian Institute of Technology, Roorkee | |
| 2. | Markus Grasmair
|
| Mathematical Sciences, Norwegian University of Science and Technology, Norway |
Abstract
In this paper, we consider 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.
Keywords
- Analysis and engineering of optimization algorithms
- Convex and non-smooth optimization
Status: accepted
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