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Proximal Operators of Sorted Nonconvex Penalties
Anne Gagneux, Mathurin Massias, Emmanuel Soubies
https://arxiv.org/abs/2506.15315 https://

Proximal Operators of Sorted Nonconvex Penalties
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted nonconvex penalties which generalizes the Sorted L1 Norm (SLOPE). These penalties are designed to promote clustering of variables due to their sorted nature, while the nonconvexity reduces the shrinkage of coefficients. Our goal is to provide efficient ways t…