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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