  The constant rank constraint qualification, introduced by Janin in 1984 for
nonlinear programming, has been extensively used for sensitivity analysis,
global convergence of first- and second-order algorithms, and for computing the
derivative of the value function. In this paper we discuss naive extensions of
constant rank-type constraint qualifications to second-order cone programming
and semidefinite programming, which are based on the
Approximate-Karush-Kuhn-Tucker necessary optimality condition and on the
application of the reduction approach. Our definitions are strictly weaker than
Robinson's constraint qualification, and an application to the global
convergence of an augmented Lagrangian algorithm is obtained.
