  Low rank recovery problems have been a subject of intense study in recent
years. While the rank function is useful for regularization it is difficult to
optimize due to its non-convexity and discontinuity. The standard remedy for
this is to exchange the rank function for the convex nuclear norm, which is
known to favor low rank solutions under certain conditions. On the downside the
nuclear norm exhibits a shrinking bias that can severely distort the solution
in the presence of noise, which motivates the use of stronger non-convex
alternatives. In this paper we study two such formulations. We characterize the
critical points and give sufficient conditions for a low rank stationary point
to be unique. Moreover, we derive conditions that ensure global optimality of
the low rank stationary point and show that these hold under moderate noise
levels.
