Separation Approach for Augmented Lagrangians in Constrained Nonconvex Optimization

H. Z. Luo (), G. Mastroeni () and H. X. Wu ()
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H. Z. Luo: Fudan University
G. Mastroeni: Universitá di Pisa
H. X. Wu: Hangzou Dianzi University

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 2, No 5, 275-290

Abstract: 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.

Keywords: Image space analysis; Separation; Saddle points; Augmented Lagrangian function (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (18)

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DOI: 10.1007/s10957-009-9598-0

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