Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming

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