  We discuss the (first- and second-order) optimality conditions for nonlinear
programming under the relaxed constant rank constraint qualification. This
condition generalizes the so-called linear independence constraint
qualification. Although the optimality conditions are well established in the
literature, the proofs presented here are based solely on the well-known
inverse function theorem. This is the only prerequisite from real analysis used
to establish two auxiliary results needed to prove the optimality conditions,
thereby making this paper totally self-contained.
