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Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems

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Abstract

In this paper, we mainly consider the augmented Lagrangian duality theory and explore second-order conditions for the existence of augmented Lagrange multipliers for eigenvalue composite optimization problems. In the approach, we reformulate the augmented Lagrangian introduced by Rockafellar into a new form in terms of the Moreau envelope function and characterize second-order conditions via the epi-derivatives of the augmented Lagrangian.

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Acknowledgments

The authors wish to thank Boris S. Mordukhovich for his careful reading and constructive remarks.

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Correspondence to Wen Song.

Additional information

Wen Song, the research of the second author was partly supported by the National Natural Sciences Grant (No. 11371116) and by the Foundation of Heilongjiang Provincial Educational Department (No. 12521147).

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Kan, C., Song, W. Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems. J Glob Optim 63, 77–97 (2015). https://doi.org/10.1007/s10898-015-0273-8

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