  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.

Optimization and Control