TY  - INPR
A1  - Harrach, Bastian von
T1  - The Calderón problem with finitely many unknowns is equivalent to convex semidefinite optimization
N2  - We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be piecewise constant with respect to a given pixel partition, and upper and lower bounds are assumed to be known a-priori.
We will show that this Calderón problem with finitely many unknowns can be equivalently formulated as a minimization problem for a linear cost functional with a convex non-linear semidefinite constraint. We also prove error estimates for noisy data, and extend the result to the practically relevant case of finitely many measurements, where the coefficient is to be reconstructed from a finite-dimensional Galerkin projection of the Neumann-Dirichlet-operator.
Our result is based on previous works on Loewner monotonicity and convexity of the Neumann-Dirichlet-operator, and the technique of localized potentials. It connects the emerging fields of inverse coefficient problems and semidefinite optimization.
KW  - inverse coefficient problem,
KW  - Calderón problem
KW  - finite resolution
KW  - semidefinite optimization
KW  - Loewner monotonicity and convexity
Y1  - 2023
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/71704
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-717043
ER  -