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.
|Autori:||Luo H.Z; Mastroeni G; Wu H.X.|
|Titolo:||Separation approach to augmented lagrangians in constrained nonconvex optimization|
|Anno del prodotto:||2010|
|Digital Object Identifier (DOI):||10.1007/s10957-009-9598-0|
|Appare nelle tipologie:||1.1 Articolo in rivista|