Solution-Set Geometry and Regularization Path of a Nonconvexly Regularized Convex Sparse Model

arXiv:2311.18438v2 Announce Type: cross
Abstract: The generalized minimax concave (GMC) penalty is a nonconvex sparse regularizer which can preserve the overall-convexity of the regularized least-squares problem. In this paper, we focus on a significant instance of the GMC model termed scaled GMC (sGMC), and present various notable findings on its solution-set geometry and regularization path. Our investigation indicates that while the sGMC penalty is a nonconvex extension of the LASSO penalty (i.e., the $\ell_1$-norm), the sGMC model preserves many celebrated …

abstract arxiv cs.lg eess.sp focus generalized geometry instance least math.oc math.st minimax paper path regularization set solution squares stat.th type