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- Title
Separation Approach for Augmented Lagrangians in Constrained Nonconvex Optimization.
- Authors
Luo, H. Z.; Mastroeni, G.; Wu, H. X.
- 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.
- Subjects
LAGRANGIAN functions; LAGRANGE equations; MATHEMATICAL optimization; NONLINEAR statistical models; CALCULUS of variations
- Publication
Journal of Optimization Theory & Applications, 2010, Vol 144, Issue 2, p275
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-009-9598-0