  The idea of partial smoothness in optimization blends certain smooth and
nonsmooth properties of feasible regions and objective functions. As a
consequence, the standard first-order conditions guarantee that diverse
iterative algorithms (and post-optimality analyses) identify active structure
or constraints. However, by instead focusing directly on the first-order
conditions, the formal concept of partial smoothness simplifies dramatically:
in basic differential geometric language, it is just a constant-rank condition.
In this view, partial smoothness extends to more general mappings, such as
saddlepoint operators underlying primal-dual splitting algorithms.
