ABSTRACT
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 1717 G.P. McCormick. Second Order Conditions for Constrained Minima. SIAM Journal on Applied Mathematics, 15 (1967), 641-652.. 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 1919 L. Minchenko & S. Stakhovski. On relaxed constant rank regularity condition in mathematical programming. Optimization: A Journal of Mathematical Programming and Operations Research, 60 (2011), 429-440.. Furthermore, we demonstrate that the condition is neither related to the MFCQ + WCR in 88 R. Andreani , J.M. Martínez & M.L. Schuverdt . On second-order optimality conditions for Nonlinear Programming. Optimization, 56 (2007), 529-542. nor to the CCP2 condition, the companion constraint qualification associated with the second-order sequential optimality condition AKKT 2 in 55 R. Andreani , G. Haeser , A. Ramos & P. Silva. A second-order sequential optimality condition associated to the convergence of optimization algorithms. IMA Journal of Numerical Analysis, 37 (2017), 1902-1929..
Keywords:
Nonlinear programming; second-order optimality conditions; constraint qualification
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