  We analyze a preconditioned subgradient method for optimizing composite
functions $h \circ c$, where $h$ is a locally Lipschitz function and $c$ is a
smooth nonlinear mapping. We prove that when $c$ satisfies a constant rank
property and $h$ is semismooth and sharp on the image of $c$, the method
converges linearly. In contrast to standard subgradient methods, its oracle
complexity is invariant under reparameterizations of $c$.
