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Saddle points of general augmented Lagrangians for constrained nonconvex optimization

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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.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    H. X. Wu

  2. Department of Applied Mathematics, College of Science, Zhejiang University of Technology, Hangzhou, 310032, Zhejiang, People’s Republic of China

    H. Z. Luo

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  1. H. X. Wu
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  2. H. Z. Luo
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Correspondence to H. Z. Luo.

Additional information

This work was supported by the National Natural Science Foundation of China under grant 11071219, the Zhejiang Provincial Natural Science Foundation of China under grant Y6090080, and the Postdoctoral Key Research Foundation of China under grant 201003242.

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Wu, H.X., Luo, H.Z. Saddle points of general augmented Lagrangians for constrained nonconvex optimization. J Glob Optim 53, 683–697 (2012). https://doi.org/10.1007/s10898-011-9731-0

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