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We propose techniques for approximating bilevel optimization problems withnon-smooth lower level problems that can have a non-unique solution. To thisend, we substitute the expression of a minimizer of the lower levelminimization problem with an iterative algorithm that is guaranteed to convergeto a minimizer of the problem. Using suitable non-linear proximal distancefunctions, the update mappings of such an iterative algorithm can bedifferentiable, notwithstanding the fact that the minimization problem isnon-smooth.

Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems