  We present new constraint qualification conditions for nonlinear semidefinite
programming that extend some of the constant rank-type conditions from
nonlinear programming. As an application of these conditions, we provide a
unified global convergence proof of a class of algorithms to stationary points
without assuming neither uniqueness of the Lagrange multiplier nor boundedness
of the Lagrange multipliers set. This class of algorithm includes, for
instance, general forms of augmented Lagrangian, sequential quadratic
programming, and interior point methods. We also compare these new conditions
with some of the existing ones, including the nondegeneracy condition,
Robinson's constraint qualification, and the metric subregularity constraint
qualification.
