We introduce quasinormality and pseudonormality for nonlinear second-order cone programming by exploiting the spectral geometry of the Lorentz cone. The proposed quasinormality distinguishes interior and boundary multipliers and, in the latter case, relates constraint violation to the corresponding spectral direction. It recovers classical quasinormality when all cone blocks are one-dimensional and is strictly weaker than … Read more
Quasinormality is a classical constraint qualification originally introduced by Hestenes in 1975 and subsequently extensively studied in nonlinear programming and in problems with abstract constraints. In this paper, we extend this concept to the setting of nonlinear semidefinite programming (NSDP). We show that the proposed condition is strictly weaker than Robinson’s constraint qualification, while still … Read more
In the present paper, we prove that the augmented Lagrangian method converges to KKT points under the quasinormality constraint qualification, which is associated with the external penalty theory. For this purpose, a new sequential optimality condition for smooth constrained optimization, called PAKKT, is defined. The new condition takes into account the sign of the dual … Read more