We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the \$\$l_1\$\$l1norm of its entries–-a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex functions, yielding a simple and unified approach for deriving inequalities balancing the various features of the optimization problem at hand, at the extreme points of the solution set.

Arxiv link: https://arxiv.org/abs/1401.4774