Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/287453 
Autor:innen: 
Erscheinungsjahr: 
2021
Quellenangabe: 
[Journal:] Optimization Letters [ISSN:] 1862-4480 [Volume:] 16 [Issue:] 5 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 1599-1609
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
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.
Schlagwörter: 
Inverse Problem
Finitely many measurements
Monotonicity
Convexity
Loewner order
JEL: 
R30
C22
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