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Many inverse problems can be cast as a PDE-constrained optimization problem with non-linear equality constraints. By enforcing these constraints, however, we are tacitly assuming that the underlying PDE model is an accurate description of the underlying process. To account for imperfect models, I propose a relaxed formulation that treats the constraints through an additive penalty. I discuss ways to design efficient algorithms through the use of variable projection and present some numerical examples.
This presentation is part of Minisymposium “MS72 - Inverse problems with imperfect forward models (2 parts)”
organized by: Yury Korolev (University of Cambridge) , Martin Burger (University of Muenster) .