This paper aims at showing that the class of augmented Lagrangian functions, introduced by Rockafellar and Wets, can be derived, as a particular case, from a nonlinear separation scheme in the image space associated with the given problem; hence, it is part of a more general theory. By means of the image space analysis, local and global saddle point conditions for the augmented Lagrangian function are investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Under second order sufficiency conditions in the image space, it is proved that the augmented Lagrangian admits a local saddle point. The existence of a global saddle point is then obtained under additional assumptions that do not require the compactness of the feasible set.
Separation approach to augmented lagrangians in constrained nonconvex optimization
MASTROENI, GIANDOMENICO;
2010-01-01
Abstract
This paper aims at showing that the class of augmented Lagrangian functions, introduced by Rockafellar and Wets, can be derived, as a particular case, from a nonlinear separation scheme in the image space associated with the given problem; hence, it is part of a more general theory. By means of the image space analysis, local and global saddle point conditions for the augmented Lagrangian function are investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Under second order sufficiency conditions in the image space, it is proved that the augmented Lagrangian admits a local saddle point. The existence of a global saddle point is then obtained under additional assumptions that do not require the compactness of the feasible set.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
