relaxed quasinormality

Quasinormality in nonlinear second-order cone programming

Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , , , , , ,

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

A relaxed quasinormality condition and the boundedness of dual augmented Lagrangian sequences

Categories Nonlinear Optimization Tags , , ,

Global convergence of augmented Lagrangian methods to a first-order stationary point is well-known to hold under considerably weak constraint qualifications. In particular, several constant rank-type conditions have been introduced for this purpose which turned out to be relevant also beyond this scope. In this paper we show that in fact under these conditions subsequences of … Read more