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Nonsmoothness is often a curse for optimization; but it is sometimes ablessing, in particular for applications in machine learning. In this paper, wepresent the specific structure of nonsmooth optimization problems appearing inmachine learning and illustrate how to leverage this structure in practice, forcompression, acceleration, or dimension reduction. We pay a special attentionto the presentation to make it concise and easily accessible, with both simpleexamples and general results.

Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications