NDLI: On Saddle Points of Augmented Lagrangians for Constrained Nonconvex Optimization

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, D. McKinnon, K. I. M. Sun, X. L.
Copyright Year	2005
Abstract	We present in this paper new results on the existence of saddle points of augmented Lagrangian functions for constrained nonconvex optimization. Four classes of augmented Lagrangian functions are considered: the essentially quadratic augmented Lagrangian, the exponential-type augmented Lagrangian, the modified barrier augmented Lagrangian, and the penalized exponential-type augmented Lagrangian. We first show that under second-order sufficiency conditions, all these augmented Lagrangian functions possess local saddle points. We then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions. The results obtained in this paper provide a theoretical foundation for the use of augmented Lagrangians in constrained global optimization. Our findings also give new insights to the role played by augmented Lagrangians in local duality theory of constrained nonconvex optimization.
Starting Page	1128
Ending Page	1146
Page Count	19
File Format	PDF
ISSN	10526234
DOI	10.1137/030602770
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	4
Volume Number	15
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-28
Access Restriction	Subscribed
Subject Keyword	Optimality conditions, duality constrained global optimization Nonconvex programming, global optimization nonconvex optimization saddle point and duality augmented Lagrangian functions
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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