Saddle points of general augmented Lagrangians for constrained nonconvex optimization

Authors:
H. X. Wu;H. Z. Luo
Affiliations:
Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, People's Republic of China 310018;Department of Applied Mathematics, College of Science, Zhejiang University of Technology, Hangzhou, People's Republic of China 310032
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

Local and global saddle point conditions for a general augmented Lagrangian function proposed by Mangasarian are investigated in the paper for inequality and equality constrained nonconvex optimization problems. Under second order sufficiency conditions, it is proved that the augmented Lagrangian admits a local saddle point, but without requiring the strict complementarity condition. The existence of a global saddle point is then obtained under additional assumptions that do not require the compactness of the feasible set and the uniqueness of global solution of the original problem.