Pseudonormality – Optimization Online

Quasinormality in nonlinear second-order cone programming

Published: 2026/10/29

Constrained Nonlinear Optimization, Second-Order Cone Programming augmented Lagrangian, constraint qualifications, error bound, nonlinear second-order cone programming, Pseudonormality, quasinormality, relaxed quasinormality

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 and pseudonormality for nonlinear semidefinite programming

Published: 2026/03/01

Daiana Santos

Linear, Cone and Semidefinite Programming, Semi-definite Programming Augmented Lagrangian methods, constraint qualifications, nonlinear semidefinite programming, Pseudonormality, quasinormality

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