A Note on the McCormick Second-Order Constraint Qualification

The study of optimality conditions and constraint qualification is a key topic in nonlinear optimization. In this work, we present a reformulation of the well-known second-order constraint qualification described by McCormick in [17]. This reformulation is based on the use of feasible arcs, but is independent of Lagrange multipliers. Using such a reformulation, we can show that a local minimizer verifies the strong second-order necessary optimality condition. We can also prove that the reformulation is weaker than the known relaxed constant rank constraint qualification in [19]. Furthermore, we demonstrate that the condition is neither related to the MFCQ+WCR in [8] nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT2 in [5].