Journal of Global Optimization

, Volume 63, Issue 1, pp 77–97 | Cite as

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

  • Chao Kan
  • Wen Song


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.


Augmented Lagrange multiplier Moreau envelope Second-order epi-derivative Eigenvalue composite optimization problems 



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


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical and SciencesHarbin Normal UniversityHarbinPeople’s Republic of China

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