SWAGGER: Sparsity Within and Across Groups for General Estimation and Recovery

Penalty functions or regularization terms which promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within arbitrary overlapping groups in a vector. We show multiple example use cases, demonstrate synergy between it and other regularizers, and propose an algorithm to efficiently solve problems regularized or constrained by the proposed penalty.