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The talks in our minisymposium discuss numerical methods and practise of imaging problems that are linked to measurements in a non-linear fashion. This linkage take, for instance, the form of a control constraint on the solution of an optimisation problem. As an example, the constraint can arise through a PDE modelling the relationship of boundary measurements to desired interior data; such imaging modalities include various forms of electrical, optical, and acoustic tomography. The linkage can also arise from the desire to optimise, to train, an inner imaging model to available true data or fitness functions. The inner model can take the form of a non-linear neural network, or an optimisation problem itself. While the former needs to mention, the latter methodology has also gained significant popularity as an approach to optimise conventional, more analytically justified imaging models to expected data.