TY  - JOUR
A1  - Harrach, Bastian von
T1  - Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming
T2  - Optimization letters
N2  - Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenges. We show that an inverse elliptic Robin transmission problem with finitely many measurements can be equivalently rewritten as a uniquely solvable convex non-linear semidefinite optimization problem. This allows to explicitly estimate the number of measurements that is required to achieve a desired resolution, to derive an error estimate for noisy data, and to overcome the problem of local minima that usually appears in optimization-based approaches for inverse coefficient problems.
KW  - Inverse Problem
KW  - Finitely many measurements
KW  - Monotonicity
KW  - Convexity
KW  - Loewner order
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63493
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-634937
SN  - 1862-4480
N1  - Open Access funding enabled and organized by Projekt DEAL.
N1  - Early View-Version: Online Version of Record before inclusion in an issue.
VL  - 2021
IS  - Online Version of Record before inclusion in an issue
PB  - Springer
CY  - Berlin; Heidelberg
ER  -