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

On strong second-order optimality conditions under relaxed constant rank constraint qualification