We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the l_1 norm 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.

## Citation

23 pages, 2 figures

## Article

View Extreme point inequalities and geometry of the rank sparsity ball