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

Abstract Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown function PDE is be determined from partial knowledge of its solutions. This usually a highly non-linear ill-posed problem, for which unique reconstructability results, stability estimates global convergence numerical methods are very hard achieve. The aim this note point out new connection between problems semidefinite programming that may help addressing these challenges. We show Robin transmission problem with finitely many measurements can equivalently rewritten as uniquely solvable convex optimization problem. allows explicitly estimate the number required achieve desired resolution, derive error noisy data, overcome local minima appears optimization-based approaches problems.