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

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  • Chao Kan
  • Wen Song

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. Copyright Springer Science+Business Media New York 2015

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  • Chao Kan & Wen Song, 2015. "Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems," Journal of Global Optimization, Springer, vol. 63(1), pages 77-97, September.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:1:p:77-97
    DOI: 10.1007/s10898-015-0273-8
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    References listed on IDEAS

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    1. R. Tyrrell Rockafellar, 1989. "Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 462-484, August.
    2. A. S. Lewis, 1996. "Derivatives of Spectral Functions," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 576-588, August.
    3. Alexander Shapiro & Jie Sun, 2004. "Some Properties of the Augmented Lagrangian in Cone Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 479-491, August.
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    Cited by:

    1. Chao Kan & Wen Song, 2024. "Second-Order Conditions for the Existence of Augmented Lagrange Multipliers for Sparse Optimization," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 103-129, April.

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