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Energy minimization methods have been among the most powerful tools for tackling ill-posed image processing problems. They are extremely versatile, are able to model the data formation process explicitly, and allow a detailed mathematical analysis of the solution properties. An alternative approach is to consider a parameterized function, a network, that directly maps from the input data to the desired solution and try to learn the optimal parameters of this mapping on a set of training data. While such learning based approaches have recently outperformed energy minimization methods on many image processing problems, several challenging mathematical questions regarding their training as well as the analysis and control of the produced outputs are not well-understood yet. The goal of this minisymposium is to bring together experts from the fields of machine learning, image processing, and optimization to discuss novel approaches to the design of networks, the solution of the nested non-convex and non-smooth optimization problems to be solved for their training, and the analysis of the resulting solutions.