# Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming

@article{Harrach2022SolvingAI, title={Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming}, author={Bastian von Harrach}, journal={Optimization Letters}, year={2022}, volume={16}, pages={1599-1609} }

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…

## 2 Citations

### The Calder\'on problem with finitely many unknowns is equivalent to convex semidefinite optimization

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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…

### Stabilizing Circulant Matrix in Modeling of Mechanical Structures Vibration using the Interior Point Methods

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